Is it obligatory to endure severe itching of the beard due to hot weather, or is it permissible to shave it? And is it better to pray in congregation at the university mosque after the lecture, or to pray in the designated prayer area within the college building?

It is permissible to trim the beard if the coarseness of the hair causes constant itching and sensitivity, and it is permissible to shave the hair growing on the neck. As for performing congregational prayer in the aforementioned zawiya (religious lodge), there is no harm in it according to the majority of scholars, though praying in the mosque is preferable.