Hello @jonthebropony !
First off, it's great to hear that you'll be enjoying your first bronycon! This'll be my second, so I can give you plenty of answers from my first.
With the hotel question, I don't really recall most hotels I've stayed at even having under 21 restrictions. It's usually just been 'are you an adult?'. But if someone else has more clarification on this, they're probably the person to ask. If you do find a need to room with someone, you can put up an advertisement here asking if anyone wants to room. Lots of folks are happy to share cost of rooms and meet new people, usually.
For the Gala, any admission ticket gets you into it, so don't worry about that. Priority tickets just enter first. As for dressware, polo and dress pants are quite well enough. It's only 'semi-formal' dress. Personally, I just love looking good, so I'll be in black slacks, a white long sleeve button up, and a vest with a tie. As long as you aren't really casual, you're guchi. If you have any questions, you can always ping a moderator.
As for looking for other folks from Tennessee, there's a thread on site where we are gathering where everyone is coming from. Check it out https://community.bronycon.org/t/where-are-you-traveling-from-the-bronycon-2017-attendee-map/5551/145
Of course a bag is plenty well acceptable, and I highly recommend one. A lot of folks (to include me) bring bags along to carry various items ranging from necessities like bottles of water and baby formulas to games and props to all the swag that they buy in the vendor hall.
I could be wrong about everything, of course, but I feel pretty confident telling you all this. Once again, welcome to the con, and I hope you have a blast!