What is the ruling on the money a student receives from his father if he attends lectures but does not pay attention to them, or sleeps during them, or is distracted from them? And is it permissible for him to look at the blackboard while averting his gaze from the female teacher whenever she appears, and is that considered among the pardoned glances that are unintentional? And what is the ruling on his inattention and lack of focus in lectures?

It is impermissible to look at a non-mahram (definition) woman with lust or fear of temptation. As for looking without lust, with the assurance of no temptation, there is a difference of opinion, and some scholars have permitted it in cases of obligatory or recommended education. If you need to look at a female teacher to benefit, there is no impediment, provided you lower your gaze as much as you can. You must seek Allah's help and frequently engage in remembrance (dhikr (definition)) and seeking forgiveness (istighfar).