What should I do about someone who prevents me from praying in the mosque and curses religion, Islam, and prayer, and what is the ruling on such an act?

Insulting religion or its rituals is a major act of disbelief (kufr akbar). You must advise your father who does this and remind him of the seriousness of his actions. If he does not respond, then there is no sin upon you as long as you disapprove of his actions, and you should avoid sitting with him when he shows disrespect towards religion. You are not obligated to obey him if he tells you to abandon prayer; instead, you must maintain your prayers in congregation at the mosque, for there is no obedience to a creature in disobedience to the Creator. Be patient with any harm he inflicts due to your adherence to Allah's obligations. If the harm intensifies and you can no longer bear it, then seek independent housing if possible. Otherwise, you must be patient, accompany him with kindness, and supplicate for his guidance.