Is it permissible to go to the mosque before one's father to avoid missing the opening Takbir, knowing that the mother requests waiting? And is it permissible to pray behind an Imam whose creed is unknown?

If the son's going to the mosque without waiting for his father does not displease them, then it is more befitting to attain the virtue of catching the opening Takbeer. However, if it displeases them, then it is not permissible, and the father must be obeyed if he orders the delay of the prayer to pray with him in congregation, as long as the prayer is performed within its prescribed time. It is permissible to pray behind any Muslim whose state is concealed, by agreement of the imams, and whoever takes the trouble to inquire about the imam's creed is an innovator.