Is what is happening to me—the failure to complete marriage and the repeated broken engagements—a result of past transgressions between me and girls? And what should I do about the girls whom I could not reach to ask for their forgiveness?

You must repent to Allah from unlawful relationships and lying. It is not necessary to seek forgiveness from the girls whom you lied to about promising marriage, as repentance from the sin of lying is sufficient. What occurred in terms of unlawful speech and touching is a sin between you and your Lord and does not necessitate seeking their forgiveness. Sound repentance involves remorse, abandoning the act, and resolving never to return to it, and it is accepted by Allah's permission, for "the one who repents from a sin is like one who never sinned." Continue in your repentance, do not communicate with them, fortify yourself with piety, and hasten to marry.