Is it permissible to masturbate to relieve sexual urges, especially when exposed to lustful stimuli and finding it difficult to control them, knowing that one is committed to fasting and that it is not sufficient to lower one's gaze?

Masturbation is forbidden, but if lust overwhelms a person and they fear falling into fornication, then masturbation is permissible to avert the lesser of two evils. It should be noted that Sheikh Al-Albani does not permit it for someone who fears committing fornication unless they resort to prophetic medicine. Furthermore, studying in mixed-gender schools is not permissible except out of necessity.