#but he would fight against them without much dilemmia

[cienie-isengardu]

Thank you for such interesting ask! And sorry it takes so long for me to answer. I needed to check out a few sources to answer as fully and coherent as it's possible. 

And yes, I do think that women were an important part of Anakin's life since the start. I would even dare to say, that his relationships with women in general were one of the most heatlhy & positive relationships he ever had. Just look at the authoritarian figures that have the biggest influences on Skywalker when he was growing up - in slavery it was Watto, then for another ~10 years Obi-Wan, Yoda & Mace Windu on one hand, on another - Palpatine. All men, and all have their own interest to keep eye on Anakin. Watto, because he was his property. Jedi, because of his connection to Force and some old, incomprehensible prophecy. Palpatine, for the same reasons that forced Yoda to take Anakin into Order. That, and desire to make Skywalker his new apprentice. And Anakin had very difficult relationships with them all. With exception of Palpatine, at least for the first decade of their familiarity (and we know that all the closeness and support given by Palpatine was a way to manipulate Skywalker through the years).

Watto constantly verbally and physically abused Anakin (and Shmi) and frankly, young Anakin all of his life was exposed to violence of any kind. When he lived on Tatooine there were few good and honorable men ("the kind that had always been in short supply in Anakin's upbringing"), what was pointed out by Vader's POV in The Rise and Fall of Darth Vader. It was Shmi alone - his mother - who loved him unconditionally. Not because he was special, or talented, or could be used so easily. She loved him even despite she didn't know herself how or why he was born ("there was no father") and being single mother in slavery must be hard thing. Anakin sometimes worried her, tested her patience and once admitted that even she didn't really know what to do with him [Roque Planet]. Still, she loved him, supported him, tried to protect him from abuse and stood up against Watto's greed that forced her son - a child! - into very dangerous podracing that no normal human had a chance to survive or finish.

Frankly, TPM movie alone showed that contast between women and men in Anakin's childhood. There is Watto, a slaver. There is Sebulba, a famous and rich winner of podracing who was quite violent and awful person ("Next time we race, boy, it will be the end of you. If you weren't a slave, I'd squash you now"). During podracing, we see Jabba the Hutt, criminal boss, who benefit from both sport and slavery. Then we have Shmi Skywalker, who despite being slave herself, taught her son importance of helping others. She may not be happy to allow her son to risk his life in dangerous podracing, but she believe he can help stranges in need and DO NOT ASK ANYTHING IN RETURN, the same as Anakin never did. There is also a old saleswoman who was warning Anakin about coming soon sandstorm, telling him he should go to home as soon as possible. And if anyone look at additional sources like books and comics, that saleswoman (named Jira) helped slaves to run away, or make sure that food for Shmi will not get wasted when her refrigerator broke down. Frankly, beside Anakin's childhood friends I don't remember that much male characters that Anakin liked or trusted or thought how honorable they were. Beside space pilot(s), who always told kids stories about space and planets and took care about them when fights began in cantina or Sebulba threatened Anakin. It's no wonder why Anakin was so heart-broken when his mother died in his arms and how guilty he felt - both for not saving her and for killing Tusken. Jedi didn't teach him how to copy with his loss, always told him to control his emotion, to let it go. Jedi made him felt unhappy though the years, and his relationship with Yoda was never good. Even Obi-Wan Kenobi damaged Anakin in many ways, like: avoiding deeply personal conversations especially about boy’s past or not understanding how slavery affected Skywalker and not showing him enough support or being too harsh, too critical to the point that Anakin felt sometimes his master didn’t trust him at all. Kenobi loved Anakin, but he never was capable to see him in different way than Jedi's.

Then we have Padme, a kind but strong-willed woman who showed him a support when he needed it the most; when he left Tatooine and mother as a scared boy, or when he killed Tusked Raiders and were full of grief and remorse. I like to think that Anakin's love for her is not based on stricte heterosexual reason (gender), but he loves her first and foremost for what kind of person she is. Skywalker said once [TCW Gambit Stealth] that Padme is the only person he can shows weakness - who allow him to be human, validate his good AND bad feelings. While others (Jedi, Republic, later Sidious & Empire) always expects him to be strong, indestructible. Of course, there is a lot things they didn't agree on or see in the same light. What mainly is rooted in their different upbringing and environments in which they grew up (slavery on Tatooine / Jedi Order vs peaceful and rich Naboo & political career). Still both grew up with the feeling that duty comes first before anything else, a sense that quite often made them push their own desire away for the sake of Republic. Padme as queen and later senator couldn't have kids or family due to lack of time for personal matters while Anakin, as a Jedi, were forbidden to love and marry because Jedi responsibilities shouldn't be corrupted by emotions. They married and maybe it was the first time they were truly selfish. Their relationship was difficult one, mainly thanks to ongoing war and forced discretion to keep their marriage a secret as long as possible. I may be wrong here, but as far as I remember, Anakin was willing to left Jedi Order for his family (and planned to do so after war for sure), but Padme wasn't ready to give up her senator role. She was scared when she told his about pregnancy. For Anakin that day was one of the most wonderful moments of his life. Padme was sure the child would be boy, while Anakin thought it will be a girl ("With a kick that hard? Definitely a girl").

I know that romance between Anakin and Padme is usally seen as awkard or boring, but I think it's worth to note that every time when Padme said she felt uncomfortable during their interaction in AotC, Anakin always backed off. Like I said earlier, Anakin grew up in abusive environment, so he was much more aware about sexual violence toward women than most of people were. Despite his feelings (and knowledge that Padme feels something toward him too) he agreed with Padme's first decision to not pursuit forbidden relationship - after that there wasn't any more flirt between them. Padme took him to Tatooine, so he could seek mother in danger and she comforted him after Shmi's death. It was also Padme's declaration of love that for truly started their relationship:

[Padme] I've been dying a little bit each day since you came back into my life. [Anakin] What are you talking about? [Padme] I love you. [Anakin] You love me? I thought that we had decided not to fall in love... that we would be forced to live a lie... and that it would destroy our lives.    [Padme] I think our lives are about to be destroyed anyway. I truly deeply love you... and before we die, I want you to know.

The words were said before their execution, but both decided to marry despite everything else. It was Padme that gave permission, and until that moment Anakin didn't try change her mind after she rejected his feeling on Naboo (”You're studying to become a Jedi. I'm-- I'm a senator. If you follow your thoughts through to conclusion... it'll take us to a place we cannot go regardless of the way we feel about each other. I will not let you give up your future for me. [...] We'd be living a lie... one we couldn't keep even if we wanted to. I couldn't do that. Could you, Anakin? Could you live like that?“).

Anakin never had many good friends in Jedi Order; he was liked in general but only few became his truly confidants. Despite that, Anakin had positive relationships:

with Thracia Cho Leem (who called both Yoda and Mace Windu on their shitty behaviour towards 12 years old Skywalker and was responsible for helping him after traumatic mission)

with Aayla Secura, who was one of few Jedi that showed Anakin support and gave advice in a way he actually could understood and I suspect their familiarity is based a lot on their awarness about female Twi'lek bad situation and violence against them.

with most(?) of female padawans/Jedi we had a chance to see him interact. Zule was the unwanted padawan, the Council dislike her (so I assume their have a lot in common) and during his time in Padawan Pack, Anakin was protective(?) about Aubrie that according to additional sources was 13 years old at that time. There was Siri, who he liked when he learned the truth about her secret mission (until that moment he assumed Siri betrayed Order and joined Krayt, a famous pirate & slaver). He showed his worry for master Tohno, who was sent for dangerous (suicide) mission. Kenobi mistook his interest as romantic one, and then were brutally reminded that Anakin's is still affected by Jabiim and his concerns are only about her well being. He tried to save her, but couldn't. There is also Legends!Barriss Offee. And what is important - for me at least - is the feeling that his relationships with women aren't sexualized. Anakin is no "macho" who flirts with every female around him (not like Kenobi, the sassy master). Padme is the only one women he loves in romantic (and sexual) way and I hope it will never be changed.

There is also Ahsoka, a padawan he was forced to take, but who became an important part of his life during Clone Wars. Ahsoka, the same as him, cared a lot for clone troopers and people in general. I wouldn't say she was for him real confidant, but she understood him much better than most masters from Council even could.

BUT!

As much as Anakin respected women, he didn't blindly idolize them. He knows that women can be evil, selfish and cruel as any other being. He lived under Gardulla's regime long enough to see how the female hutt* mistreated slaves, what included killing them for fun or as the show of her power. Asajj Ventress was one of the most dangerous foes he faced during Clone Wars. In animated series Clone Wars [2003] he killed her in rage during battle, after she murdered clone trooper unit that Obi-Wan sent after Anakin while in Republic series he killed her to protect his and Padme's secret marriage. There wasn't any doubt or attempt to explain her behavior - you know, the standard formula she is woman, she must be just hurt or misjudged, because woman are good and kind by nature and just need help of hero. She tortured Obi-Wan (and Alpha), she killed Jedi and Republic troopers, Anakin definitely didn't like her. It was Obi-Wan who wanted to redeem her and was quite obsessed about that. He even guilt tripped Anakin, because Asajj's life could be his own fate if Jinn didn’t find him before Sith.

Any slaver, male or female, was despited by Anakin the same (though I would need to look at TCW comics Slaves of the Republic again, to see how his relationship with the Queen went there).

Frankly, there is so much thing to talk about Anakin's relationship with women, but to not bore anymore, I generally think that female characters played a big role in his life. He respected women and didn't see or treat them as objects. He was aware about various kinds of violence against them, including the sexual ones. Frankly, I don't remember much scenes when Skywalker invaded personal space of people he wasn't close with, and it's not just about women. Anakin never striked me as person fond of touching other or being touched by others. He admired kind women (Shmi, Jira, Mazzie) - because kindness and helpfulness are traits he very appreciated and had himself but at the same time I don’t think he told a woman (or anyone, really)  that she should be kind and nice or obedient (beside the standard Jedi’s “follow my/Council orders” toward Ahsoka and even then he tried to teach her that following order doesn’t mean she can’t be creative about the way she is doing demanded things). What was seen with Zule for example. When she made a comment about clone Alpha at the war meeting, Skywalker didn’t ignore her behaviour, but didn’t say she should be more nice either. I guess, Anakin understood that not everyone can be so detached from feelings like Yoda or... Kenobi. What is worth to note, a lot women that affected his life were brave and willing to fight for what they believed or for their families.

Anakin was also very affected by violence toward women (and children) or by their death. Maybe it partially was rooted in his childhood experiences when women were the kind but also mentally strong adult figures in his life and partially because Skywalker never copied well with Shmi's death. So women (espiecially those older) reminded him of his own mother he couldn't save. Sometimes he was aware of that connection, sometimes it hit him by suprise. I also have the feeling that Anakin relationship with men (especially male figures of authority) are harder due to growing up on Tatooine full of scums and slavers who were mostly men. I may be wrong here, but I think that happens a lot in real life, that men who grew up in abusive families & environments tends to be more protective towards women, more respecting them than men who try to contol (once again) their life.

It's also worth mention that no matter how Anakin changed because of dark side, as a Vader he treated people around him the same - with pragmatic brutality. Vader killed a lot characters, regardless of race and gender, sure. But I personally  don’t remember him killing any female characters with more gore than he would kill any male counterpart. Vader's violence  toward women is not sexualized and I hope it will never change. We seriously don't need any more creeps like that, the pop culture is already full of that  trends.

Also, Vader had a lot disciples, and many of them were females. Not sure how new canon presents Empire’s view of gender, but back in the old days, a lot imperial women were discriminated due to sexism. And Lord of the Sith never cared for race or gender, he cared only for results and skills. And some of his best (trusted) agents were women, including Shira Brie a.k.a. Lumiya. Not to mention difficult relationship between Vader and Leia, because there is so much to talk about!

So yeah, Anakin had interesting relationships with various women. Even as a Sith. But that he respected women (for kindness AND mentally strength) doesn't mean he wouldn't hurt or kill them if they were his enemies.

* to be fair, I'm not sure how TCW/new canon works around gender of Hutts, because in EU members of this space could switch their gender whenever they liked.