Is it permissible to pray behind my brother, despite my doubts about his ritual purity due to him watching pornography, and what is the proper way to advise him and remind him of the obligation of ghusl if he is unaware?

Your brother has mixed good deeds with bad ones, and he needs to be advised to repent. You can advise him indirectly by giving him a pamphlet or a tape about lowering the gaze. As for his prayer, the default is that it is valid. He can be guided to the Islamic rulings through pamphlets, tapes, lectures, and reliable fatwas. Your prayer behind him is permissible, as the default is that his prayer is valid until proven otherwise.