What should we do about a father who does not pray or fast, consumes people's money unjustly and through usury, curses religion and the divine essence and scholars, treats his family harshly, and beats his wife and children? Does Islam permit him to do that?

Islam does not permit parents to oppress their children. Rather, it commands them to protect and care for them, and it has established rights for children upon their parents. Cursing religion or God is clear disbelief. The son should pray for his father's guidance and advise him with wisdom and good admonition, exercising patience with his harm. However, if he cannot escape his harm except by limiting interaction and confining it to the bare minimum of connection, then there is no blame in that.