It may be better that you put all your questions in one post so you do not have to wait for a response.
In BNCOC, I lived in a suite and we had internet for our personal laptops (we had to pay a fee). I figure that may be the same for recruiter school. I could not comment if you would have an actual room mate.
You will have a roommate and the hotel should have Wi-Fi (depending on which one you stay at, the Holiday Inn Express on Two Notch had free Wi-Fi). It might be easier to bring a laptop as opposed to a desk top but you can also sign out a laptop from the school house but they are extremely slow. I also wouldn't suggest this because it is a gov't computer and you are still responsible not going to certain websites that the Army doesn't allow.