Is it permissible to pray in a mosque that contains a grave, or in a mosque whose imam is an innovator, or in a distant mosque that one's father prevents one from attending?

It is permissible to pray behind an innovator as long as their innovation is not one that constitutes disbelief. It is not permissible to pray in a mosque that contains a grave. It is not permissible to disobey one's parent regarding going to a distant mosque when it is possible to pray in congregation in a closer mosque or at home. Therefore, the mosque whose imam is an innovator is the one where prayer should be performed if his innovation does not constitute disbelief.