You can get the information stright from the horse’s mouth at the INS website http://www.ins.usdoj.gov/graphics/services/visas.htm
Scroll down to the F visas (Academic Students) and you have plenty of links. One of the linked pages says
So, it seems to me, the school or place of study needs to be acredited with the INS and the best thing is to ask the school directly if they are, in fact, accredited. If they are, they should be able to help you. If they are not, then. . . . tough cookies I guess.
Since you mentioned in another thread that you’re planning to marry an American, I’m not sure why you need this visa anyway. Why not just go in on a fiancé visa?
If you do apply for the F though, I’d strongly recommend you don’t mention the American fiancé(e) to any INS/State Dept officials. They have a habit of not issuing non-immigrant visas to people they think plan to immigrate.
Pell Grants are US government grants given only to US citizens so that they can gain some measure of higher education. (They are useless for college, though, tuition at a decent school comes to $20,000 - $30,000 per year, and a Pell grant might come to $1600 a year).
It’s not necessarily the case that you have to spend that much per year to go to a decent college. Private institutions will cost that much, but in-state tuition for state universities may be a quarter of that or less, depending on where you go. I went to the University of Wisconsin (a respected university, not “Ivy League” but highly rated in many subject areas) about 10 years ago, and think in-state students paid under $3000 at the time. Checking their website now, I see tuition is just under $5000 for in-state students.