Are hymen repair surgeries forbidden? What should I do with the young man with whom I made a mistake and who wishes to fix what happened? And should I agree to marry another young man and lie to him about the hymen repair surgery?

The most important thing to do is to repent to Allah from zina (fornication/adultery), along with performing many righteous deeds that expiate sins. As for hymen repair, it is not permissible due to the serious শরعي (Sharia-compliant) issues it entails. If your family forces you to do it, then they must repent. If you marry someone other than the one with whom the sin was committed, then conceal what happened from him and use allusive speech (tawriya). As for marrying the one with whom the sin was committed, there is no harm in it if he has repented, but it is advisable to avoid it if one of the parents disapproves.