Is it permissible to delay prayer beyond its prescribed time for the sake of studying, and can missed prayers be made up, and what is the ruling on absence from the mosque in this case?

It is incumbent upon a Muslim to make prayer their top priority, giving nothing precedence over it, for preserving prayer on time is among the greatest causes of success, and neglecting it is a cause of failure. There is no excuse for delaying prayer beyond its prescribed time due to studies; rather, it is obligatory to hasten to pray when its time is due. Delaying prayer beyond its time is a great sin, and it must be made up according to the majority of scholars. Congregational prayer is obligatory for adult men, and it suffices anywhere. So, if you pray in congregation with your family at home, you have fulfilled your obligation, even if you miss the reward of going to the mosque. As for praying alone when one is able to pray in congregation, it is a sin according to those who deem congregational prayer obligatory, and this is the prevailing fatwa, but the prayer itself is valid and fulfills the obligation.