Do you need a ssn to further your education, and get a scholarship or financial aid

For financial aid, more than likely yes. Especially financial aid from the governemtn. But, many external scholarships do not require a SSN.

I'm not sure about needing it to further your degree, but I do know that many colleges have a place to write in your SSN or green card number on the application.

Yes you will, in factyou will need one to get into most colleges