Let's say i don't have permission to work. Can i still apply for a social security number?
Sure. If you are in that scenario, you can still apply for a SSN under certain circumstances, such as requested for a federal or local law in order to get some assistance benefit.
I see, thanks. And being a non citizen, what documents i would need to apply, please?
Well, you'll need to show you current inmigration document, as specific as it get, you need Form I-551, Immigrant Visa and I-766, EAD or work permit.