and for F-1 students what documents are needed?
You'll need to show us the  I-20 Certificate of Eligibility for Nonimmigrant Student Status.
What I'm legally able to do if I still don't have permission to work.
You can still get many benefits and services without a Social Security number. You can conduct business with a bank, register for school, get private health insurance, apply for subsidized housing, among other things.