What is the ruling on the procedures mentioned in the Qur'an memorization house, and what is incumbent upon me to do regarding them: is it to offer advice, or to stop studying there, while mentioning the evidence and the names of the muftis?

It is better for you to pray in the mosque, but there is no harm if you pray in congregation at home, as this is not objectionable, except that you miss out on a great reward. As for dedicating a specific dhikr for the conclusion of a gathering, this is an innovation (bid'ah). We advise you to adhere to the reported supplications, and what has been reported for the conclusion of a gathering is the supplication for the expiation of the gathering (Du'a Kaffarat al-Majlis). Gathering for dhikr and supplication should not be made a continuous practice, except for what has been reported, and that has been reported for the conclusion of the Qur'an, not for every Qur'an memorization circle. It is obligatory for you to object to them in this matter and not to participate with them in this reprehensible act. Rather, urge them to conclude the gathering with the legislated supplication. If they refuse, then do not participate with them, but do not stop memorizing the Qur'an with them, unless you find a place for memorization that is closer to adhering to the Sunnahs.