My son (CT) goes to college full time in PA. Worked at the university last summer. Is he a full time or part time resident of the state he goes to college in?

If you are claiming him as a dependent on your tax return then you are allowed to say he lived with you all year.  Living away at school is a "temporary absence."   If he earned money while he was in the "school" state, he may need to file a non-resident tax return for that state and a resident tax return for PA.  But we would need to know what state he was in.  PA has reciprocal agreements with several states, and there are some states with no state income tax at all.  

It depends. College dormitories, fraternity houses, sorority houses and off-campus rentals by students enrolled in college or universities do not qualify as permanent abodes, so if that is where he was living he was a nonresident. Even if he was a non-resident, he still would need to file a tax return for the income he earned in PA.

See more information about residency here: Determining Residency for PA Personal Income Tax Purposes