Is it permissible for the Imam to stipulate that the Muezzin pay a portion of his salary to cover the expenses of the mosque's worker, renew his residency permit, and pay for his travel tickets, and to allow tenants to remain in the Muezzin's residence for a rent less than its market value, knowing that the mosque is governmental and there is another employee who does not work but receives a full salary?

The Imam has no right to obligate you to anything, as he is an employee just like you, and you should refer to the Mosques Department. It is not permissible for the Muezzin or the janitor to take a salary without performing their duties. It is not sufficient to hire someone else to do the work unless the responsible authority approves. This act constitutes consuming wealth unlawfully, and it is more severe than what Sheikh al-Islam Ibn Taymiyyah mentioned regarding the mosque janitor hiring a foreign worker.