Should a young man proceed with marriage or complete his studies, and is performing Istikhara permissible in this matter?

Marriage is a good deed that should be initiated to protect oneself from the unlawful and fortify it against temptations. It may even be obligatory for one who fears temptation for himself and is capable of it. It is also one of the reasons for Allah Almighty's aid. If marriage is obligatory for you, then do not perform Istikhara concerning it; for Istikhara is performed for recommended and permissible matters, not obligatory ones, and it is not performed for the root of a recommended matter except in cases of conflict.