I can clear some of these questions up, as I had some of the same ones and found it hard to find the answers last year.
Once you have submitted the FAFSA, you are pretty much done with your end of the process. You now have to wait for the school you will be enrolling in to send you the aid package which describes how much stafford you will get. They usually will also include the paperwork/contracts that you have to fill out to get the loan from the lender the school uses. (Don't worry about it, it's nothing external. Most schools simply use a specific lender, you shouldn't have to pay any fees or anything). I didn't get this packet until June I think, or maybe later.
Once you get that packet, you "should" get your loan pretty early in the semester. In my case I got it a couple days before it started. Either way, the school will push back your tuition payment until you get your loans, they understand the process.
So if I were you, I would call your school's financial aid office and ask when the packets/offers are coming out to you. In addition, another helpful thing is to ask if they have direct deposit. This usually saves you a couple days and from having to wait in a huge line once checks come out.
Good luck
