Is it permissible for me to perform Hajj on behalf of my father, who used to drink alcohol and not pray, given that I am unsure of his repentance before his death? And will the reward reach him, and will I not incur sin?

We advise you to perform Hajj on behalf of your father for several reasons: First, the majority of jurists believe that one who abandons prayer due to negligence is not an infidel (kafir) in a way that expels him from the religion. Therefore, after his death, he is treated as a Muslim. Second, you have no certainty about how your father's life ended, or whether he prayed at the end of his life or not. Third, some of those who consider the ترك الصلاة (abandonment of prayer) to be disbelief stipulate that for it to be considered disbelief, the person must be invited to prayer and then refuse and insist on not praying. Fourth, even if one adopts the view that the disbelief of one who abandons prayer out of laziness expels him from the religion, a person might have an excuse that we do not know of, or he might have lived in an environment ignorant of Islamic rulings, or among people who do not consider the abandonment of these matters to be disbelief. Thus, his case remains doubtful.