Does studying count as an excuse for being late for Friday prayer? And is it advisable to request the establishment of a prayer room and mosque for the school (without a minaret or dome), with the possibility of the sermon being delivered by one of the students, memorizing the sermons of the sheikhs?

It is not permissible to study or be preoccupied with it after hearing the call to Friday prayer. One must leave it and hasten to the prayer. As for establishing Friday prayer in a school, it is not a condition for it to be in a mosque. However, it is not permissible for Friday prayer to be held in multiple locations within the same town unless there is a need determined by the ruler. It is not permissible for you to establish Friday prayer in the school as long as you are able to perform it in the mosque. If the school administration prevents you, then refer the matter to the competent authorities.