Hey there, and welcome to FFXIV! It's always good to see more new folks comin' in. As far as your questions go, uh...
1.) I don't think any kind of census was ever taken on this (and I can only speak for Balmung), but I can say with certainty that everywhere you go, there WILL be RPers and nonRPers mingling together. There are certain areas where you see more RPers (such as bars/taverns in the game), but there seems to be a relatively even split? I generally assume there's usually more nonRPers afoot. I think both servers are fairly open to new folks, the hardest part would be getting a new character on the server during openings. Balmung's openings tend to be really late at night (like anywhere between 11PM PST-5AM PST, depending on the day of the week).
FYI, there will always be elitist players on a server regardless of which one you choose, but in my experience, Balmung has the friendliest and helpful of the lot.
2.) Lalas are making a comeback, but other than that, miqo'te and hyur are the most prominently played races in the game (particularly for Balmung). Gender distribution between those two races is kind of even, from what I've seen? That aside, you should pick what -you- want to play. If you've got a great idea for a character and it's going to be miqo'te, then shoot for it. If you want a Roe, then go for the gold! o/
3.) Have fun, get ready for whacky adventures, and don't be afraid to approach folks. The Final Fantasy series generally has lore focused on crystals and magic with a focus on character development, so expect to see some of that here. There's a ton of lore and information regarding the game on the site, as well as many folks who can help you ease into RP in the game. The world is your oyster! o/
I hope you enjoy your time in the game! It's a good way to unwind from exams. =w=)b
Edit: Oh, someone already beat me to it. But yes, basically what Faye said.