Ninevah

As long as you can show that you (or your assistanship, fellowship, etc.) can pay for your study, you'll be fine. As you said, your I-20 already shows that. If they ask you "ties to your country", you don't have to PROVE anything (and how could you?) . Just tell them that your family is there, and that you plan to work there. That's enough.

That's enough for a SSN. You'll need to pay taxes on the stipend and this is the way IRS (the tax people) keep track on you. Your school will explain you how you get the SSN - it's not hard, you just fill some documents and then wait for the card with the number. Which reminds me, when you fill out the payroll documents on campus MAKE SURE that you or the payroll person check whether your country has some kind of a tax treaty with the US - this can save you some bucks.