It depends on whether you have been in US for 5 years

or more. Go to IRS website to find the document about resident alien or non-resident alien. If you can not find, call IRS and they are really nice.

If you are in US less than 5 years, during OPT, you don't pay social security and med. If you are in US 5+ years, you have to pay.

The first $5000 you earn does not need to pay tax, it doesn't relate how long you have been here. As long as you are holding F-1 visa, you are qualified.

That document tells you everything.