What should an Imam and preacher do whose salary is insufficient, and who fears that if he takes on additional work, he will fall short in maintaining all the prayers in the mosque, knowing that he already maintains one or two lessons and the Friday sermon?

If you can combine the additional work with your official work in the mosque, then do so. Otherwise, additional work is not permissible if it affects your work in the mosque and violates the terms of the contract, for Allah Almighty says: "O you who have believed, fulfill [your] contracts." So, either you reconcile between the two jobs, or you seek permission from an authorized official in the Ministry of Endowments, or you leave the additional work and commit to the mosque, or you leave the work in the mosque if the other work is more beneficial to you. Giving lessons does not affect the ruling, for the contract is the decisive factor, and Muslims are bound by their conditions.