Is it incumbent upon a Tunisian first-year university student in a mixed-gender university, who lowers his gaze, to discontinue his studies or to persist, taking into account various alternative employment options and their risks, and his desire to mend his relationship with his parents and kin?

What you have mentioned about disobeying one's father, severing ties of kinship, and abandoning prayer are grave sins that necessitate repentance. Allah forgives all sins for those who repent. As for the mixing of men with non-mahram women and shaving the beard, these contradict repentance. Therefore, we do not advise you to continue studying or working in a mixed environment or one that requires shaving the beard, except in cases of extreme necessity, such as being unable to achieve a minimal decent life. In case of necessity, choose the lesser of two evils, such as vocational training schools with less mixing, or shaving the beard if that is lighter than falling into the temptation of women.