Can I get Genius Bar Support w/o Applecare/Warranty? If it is past my one-year warranty, or if I just don't have AppleCare, will I still be able to get Genius Bar support?

To what extent does that support cover? I'm trying to decide whether or not I should get AppleCare, as the price is quite steep. However, I think this laptop (Air) will stick with me for quite a while.

Furthermore, will Genius Bar cover Boot Camp issues? (Like, if I'm trying to install Windows 10)
Yes, you can. Without AppleCare, advice is free; quotes for repairs are free, but the actual repairs are not.

With AppleCare, you're covered for pretty much any repair, except when caused by you: e.g. LCD backlight fails? Repaired free. Dropped your MacBook and broke the screen? Not covered. You pay.