Is it permissible to pray at home and then go to the mosque and pray behind the Imam with the intention of a supererogatory prayer, or to pray a supererogatory prayer behind him with the intention of not following him, knowing that praying behind him is not permissible and there is no other mosque, and he cannot be advised or removed?

Congregational prayer is obligatory for men, and it is not permissible to abandon it. Your prayer is valid behind the mentioned Imam, especially if you cannot find anyone else. Do not pray the obligatory prayer in your home, and do not pray behind the Imam with the intention of not following him. As for the Imam's presence only for Dhuhr and Asr prayers and his absence from other prayers, this does not prevent following him.