Is it permissible for female students to eat or use their phones in the college prayer room (musalla) under the pretext of overcrowding in the cafeteria or due to their shyness about eating in front of male students?

There is no harm for female students to eat in the room designated for prayer. Eating in the mosque is permissible if its cleanliness is ensured, as evidenced by hadiths, including the companions eating bread and meat in the mosque, and the dwelling of the People of the Suffa therein. Similarly, it is permissible to talk on a mobile phone inside the mosque, provided that it does not harm or disturb those praying, and this is even more permissible in the aforementioned room. The default for a Muslim is safety and good faith in them, and if it is known that one of them does not pray, then advising her becomes obligatory.