1) That should be fine
2) It depends. Were you taught by the prof you are doing the social science research with?
3) I guess you could, but from my understanding, post-doc letters don't carry much weight
2. If the letter requires a letter from a professor, it must be from a professor who taught you in a class. Most schools I've seen usually differentiate "character" letters (i.e. from PIs, bosses, volunteer coordinators) from professor letters. If your PI also was your professor, I don't see why they can't write a superb letter talking about class and out of class experiences. Then you can probably submit the letter under whichever category you need!