Is it permissible for the director of Quran memorization circles to take extra money beyond the costs of trips, or to take what suffices him from this money, or from students' subscriptions, due to the absence of a salary for his work?

You are not permitted to take any of this money, as you are entrusted with spending it for the purpose for which it was given, which is to organize trips for students. Therefore, it is not permissible for you to spend it on anything other than what it was designated for, due to the words of Allah Almighty: (Indeed, Allah commands you to render trusts to whom they are due). You are obligated to return any surplus or keep it for its owners until you spend it on the purposes for which they provided it. The fact that you do not receive a salary does not permit you to commit betrayal. Rather, you have the right to demand compensation for your work, but you are not permitted to take anything from the workshop fees either. Your obligation is to fear Allah and beware of consuming unlawful wealth.