Is it permissible for a Muslim girl to marry a Christian young man who promised to convert to Islam, given that transgressions occurred between them before marriage? And what is the ruling on repentance in this case?

Repentance is obligatory. Therefore, you must offer sincere repentance, cut off your relationship with this young man, and strive in righteous deeds, for your evil deeds may be replaced with good ones. There is no harm in marrying this young man after your repentance and after you have verified his true Islam, and you must be keen on guiding him. You must conceal your past sins and avoid residing among polytheists.