Is it permissible to celebrate a young man or woman reaching the age of 21 by reciting the Quran, cooking food, gathering, and giving a key to the one being celebrated?

What you mentioned about celebrating and reciting the Quran when a young man or woman reaches 21 years of age has no basis in Islamic law. Rather, it is an innovation (bid'ah) and an imitation of Christians. The Prophet said: "Whoever does an action which is not in accordance with this matter of ours, it will be rejected." And he said: "Whoever imitates a people is one of them."