What causes the glans of the penis to stick together after attempting to lower one's gaze, and does this indicate the emission of pre-seminal fluid (madhiy)? Also, how can one verify the emission of pre-seminal fluid before prayer in a mixed environment like a university?

Madhī (pre-seminal fluid) is a thin, white discharge that exits upon usual pleasure, which is inclination towards something accompanied by erection during playful interaction or recollection. If you do not feel stimulation that causes the discharge of madhī, there is no evidence of its exit, and you are not required to inspect. It is sufficient for you to act upon the original principle, which is its non-exit. If you are certain of its exit, purify your body and clothes from it and perform ablution (wuḍūʾ). If you see it after prayer, it is attributed to the nearest time its exit is probable, and your prayer is valid if its exit is probable after the prayer. Lowering the gaze is a great act with immense benefits, and it is aided by striving against the self and restraining it to this. Seek a non-mixed university, and if that is not possible, choose the lesser of two evils, and be keen on lowering your gaze and avoiding religious transgressions.