Your chances of TPS being approved in timely manner depends upon whether or not you've filed taxes in the last three years --whether as a resident or non-resident. And yes, you can still file taxes if you're in a non immigrant visa like F-1. You don't have to pay social security and Medicare taxes though.

I kind of realized this after a friend of mine filed a petition for Greencard after he was approved for asylum. His application was delayed for almost 8 months and after he filed taxes (was on F-1 & never filed taxes before) --within a month his card arrived in the mailbox .

So folks, Pay taxes-live better.

Good Luck to everyone.