Is giving money to an employee after completing the school registration process, based on his request for "coffee," considered a bribe, and what are the consequences of that, and is it obligatory to leave this school?

What was paid to the worker is not a bribe, but it is from the forbidden gifts of workers, and it should have been refrained from paying it. The employee must perform his work fully without demanding a مقابل (consideration), and whatever he takes in addition to his salary without the permission of his employer is forbidden, as stated in the Hadith (definition): "The gifts of workers are ghulul (ill-gotten gains)." As for studying in school, there is no harm in it.