What is the ruling on shaving the beard for entering university, and is it considered a sin in this case? And how can one deal with the mixing of genders in mixed Egyptian universities?

Shaving the beard is forbidden (haram) and is not permissible except out of a compelling necessity or a general need that takes the place of necessity. So, if a student is compelled to shave his beard to study at a specific university where he cannot study otherwise, or if there is a need for the Ummah for righteous individuals to be in certain specializations, and they are prevented from studying except by shaving their beards, then it is permissible for him to do so. The benefit resulting from righteous people taking on positions and jobs is greater than the benefit of growing the beard, and the harm of their turning away from specializations and corrupt individuals taking them on is greater than the harm of shaving the beard.