I have an iPhone 7 .. can I come in to have my battery replaced?

Yes

Yes they will replace it for a fee. See website for details

Absolutely. Apple started offering battery replacement for only $29 since coming out with the reason why they slow older devices. You have an iPhone 7 which is new model, I suggest that you make an appointment with the genius bar to have them look at your phone, in most cases they will take your phone and give you a new one on spot if the screen is not cracked of course. If that's something you want I suggest you back up you device through the cloud or iTunes. Good luck

Probably. It's a 24 hour store with a full repair room. Think they would be able to help.