Yes, many lights work off the battery of the travel trailer. Yes the water pump works off the 12 volt battery, hence you can flush a toilet.
The bigger question is, since you are a Newbie, what are you considering to buy? size? and what do you plan to pull it with.
We can give all sorts of advise, but we don't know if you plan to stay in a 18-25' trailer you pull with your F150, or a 26-33' trailer you pull with a F250 (or equivalent).
The BEST advise I can offer is, educate yourself, as you have started to do. Learn about trailers, ask questions on a site like this one, many experienced people. And look at trailers. Caution: Trailer Sales People have a terrible reputation (lower than a used car salesman) as far as knowledge, and telling you things that are not true, especially that your ABC car/truck can pull DEF trailer with no problem at all. You say Yosemite, I've been there. Awesome. I pull a 20' Travel Trailer with a 2005 Yukon XL, and would find it marginally acceptable out in the mountains and long inclines.