A lot of the questions you asked vary from chapter to chapter. I've just found out myself that some
chapters do require you to be a major or minor, but on a national level, it is not a requirement.
As to whether you can be in an NPC and DO... that varies from chapter to chapter too. My chapter had a by-law against it, but it is not a national rule. Nationals DOES state that you can not be a member of DO and SAI. A lot of it comes down to whether the chapter in question views itself as a professional group or a social sorority. My chapter (when I pledged) was a very social group, did a lot of things with the other greeks, and once upon a time, was on panhell at our school. However, by the time I left school, the membership had turned, and operated as a professional group and never did anything fun (sorry...little bitter there)
Yes, our national website is crap

I get so jealous when I look at all the beautiful websites some other national (and local!) sororities have

If I knew anything about building a webpage I'd volunteer to re-do it in a second!
Are we co-ed? That is a BIG issue of tension

Due to our status as a professional organization, we were forced to admit men beginning sometime in the 70s. However, in my experience at least, male members are VERY uncommon. There was a guy in my chapter when I pledged, and he didn't stay active very long, because everyone (not the DOs... I mean other people on campus) made fun of him for being a guy in a sorority. So I wouldn't worry about that much... most guys, if they want to be in a music GLO will join Phi Mu Alpha. At our national convention (which was held in GA... I'll get to that in a second) I heard a statistic quoted that less than 2% of membership internationally is male, and that comes almost entirely from a couple of chapters that are almost all male.
Yes! There are chapters in GA... I'm not sure where exactly... our last Triennial Convention was held at the University of Georgia, and was hosted by a chapter in that area somewhere... I'll have to look at my information from convention and see if I can find what school it was at.
You have no idea how thrilled I am that someone is asking about DO!! I think I'm the only one on the board, so it's nice to be feelin' some love