Is it permissible for the mosque's Imam to continue leading prayers in his mosque alone or with one person, or should he move to another mosque? And to what extent is he entitled to his salary after the worshippers have left his mosque?

My view is that he should stay, but there must be another person with him. If no one is available, he should go to another mosque to pray with the congregation. As for the salary, the officials must be informed, and their permission obtained.