Is it permissible for a student to boast about his prayer in front of his classmates in order to encourage them to pray, and is it permissible for them to call him a hypocrite?

Your colleagues are not permitted to accuse you of hypocrisy for advising them to abandon evil deeds. Rather, they must accept your advice and thank you for it. As for showing off your prayer in front of them, this is not the ideal approach. It is sufficient for you to advise them by explaining the importance of prayer and the danger of abandoning it, and by informing them of the scholars' statements warning against negligence in it, as well as against mixing with and touching foreign women. This is more beneficial, more likely to be accepted, and further removed from showing off.