Is it permissible to give a portion of the mosque's funds to its caretaker (Qayyim) or to those who perform work in it, as a form of assistance, knowing that he receives a salary from the Endowments Authority?

There is no religious impediment to paying a portion of the endowment's funds to the mosque's caretaker if he is in need or if his salary is insufficient, as this serves the interest of the mosque. This is unless the endower stipulated that the money be spent on specific matters that do not include the mosque's caretaker.