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.
What are the other option of documents that I can submit if I don't have one of these specific documents in applying for a Social Security Number?
Do you have the Employee Identification Card?