Questions on Female Characters from a Male Writer

Hey everyone. I realize this is probably poking the hornets' nest, but... today I come to you as an artist and writer, with some serious questions that I've been trying to wrap my head around recently. I know that these days, sexism and feminism are sort of heated and controversial topics on the internet. There's been a lot of material circulating as of late about sexism in comic and gaming culture. I don't really want to upset anyone, but I do have some things I've legitimately been wondering, and if we could start some sort of rational dialogue about it, I would gladly welcome your thoughts.

As most of you who follow me know, I am male. I also have Asperger's syndrome, which I believe is relevant in this discussion insofar as I tend to have difficulty with empathy, and with fully understanding points of view that are not my own. In my writing, I've noticed that this is reflected by the fact that my major protagonists pretty much always have a lot in common with me-- generally introverted or struggling with social anxieties, sometimes misanthropic, usually artistic in one way or another... almost always male. I write what I know, because I feel like when I attempt to develop characters that aren't what I know firsthand, they come off as insincere and flat. I feel like I don't have the insight necessary to speak for anyone but myself. As a result, the prospect of writing a main character who is radically different from myself is daunting to me-- someone who has different religious beliefs, for example, or a different ethnic background, or someone who is much older or younger than I am. But I think the issue that is most challenging for me is writing good female characters. As an author, I feel like it's a big weakness of mine, that I don't feel comfortable developing 100% original characters with a wide range of perspectives, beliefs, priorities and insights; when I do write female characters, I find they're mostly based on real women in my life, with a bit of creative embellishment. I've been thinking about how to write female characters specifically a lot lately, probably because the recent controversies seem to indicate to me that this isn't just me-- society as a whole is struggling with this too.

So here are my questions:

1) How does a male writer develop authentic female characters (particularly a male author like me, who has difficulty seeing the world from eyes other than his own)? Especially for those of you who are female, what sorts of characteristics do you think aren't exemplified enough in female characters in popular fiction written by males?

2) Whenever you read a piece of fiction, how much do you think the author's gender enters into your consideration of the way the story has been written, and particularly the way the relationships between characters are treated? I mean, I think it's fair to say that there's a definite disparity between, say, Jane Austen and Ernest Hemingway, but I feel like those are the extremes. Do you think not knowing the author's gender beforehand would make a significant difference in your perception?

3) Are there any others here who feel like they have a difficulty writing characters of the opposite gender? If so, how do you deal with it? I'm particularly curious to hear if there are any ladies here who struggle with male characters. 

4) In regards to visual media like comics-- how does a male writer or artist create universally respectable female characters appealing to anybody? I don't really want to alienate either gender, but sometimes, it honestly feels to me like a "damned if you do, damned if you don't" situation because (in general) they seem to want different things in the media they consume. The whole male gaze issue in particular seems to be a major wedge which has started thousands of flame wars. Can (for lack of a better term) "fanservice" for certain male readers coexist simultaneously in the same continuity with more progressive attitudes regarding women and female empowerment, or is it too much of a contradiction?

5) And finally... is it even possible for male writers or artists to escape insinuations of contributing to our societal androcentrism, or is it simply an inherent judgment we have to accept (regardless of how progressive the attitudes toward women in our work may be) just by virtue of being male?