Upvote:2
It's not quite clear how long you're staying and what exactly you're studying, but the State Department breaks it down for you (emphasis mine)
For short periods of recreational study, a Visitor (B) visa can be used Enrollment in a short recreational course of study, which is not for credit toward a degree or academic certificate, is permitted on a visitor (B) visa.
However you're going to need an F visa if you're going to study somewhat more seriously, which I think is more likely based on the wording of your question.
Another academic institution, including a language training program
For your other questions, any visa application will ask you to provide accommodation details so yes you should provide that as well as your invitation letters to demonstrate what the purpose of the trip is.