"قَلَم اَلْأُسْتاذة بُنِّيّ."
Translation:The professor's pen is brown.
Does this mean there is no way to mark possessive for 3rd person full nouns? ... Also, how would you say "a professor's pen"?
a professor's pen: قلمُ أستاذٍ
if you by 3rd person possessive like (his pen, her pen) then it is possible of course. That would be (قلمُهُ, قلمُها) respectively (respectively from right to left).