Is it considered just for a principal of an Islamic school to treat some employees differently (financially and morally), knowing that some of them bear the burden of Da‘wah, and is it permissible for him to give money to an employee without work while compelling another to perform his work for the same salary?

If the school principal is its owner, then his actions regarding it are not considered unjust, and he has the right to choose employees and determine their wages. However, if the school is public and he is responsible for its administration, then he must fear Allah and establish justice and equity among his employees; because favoritism among employees without a valid reason is manifest injustice and a grave sin for which Allah has warned those who betray their subjects by depriving them of Paradise.