Do the vows made between a young man and a young woman to marry, which led to sexual practices without intercourse, find acceptance with Allah, or is this relationship considered forbidden?

These sinful relationships are forbidden because they lead to committing greater forbidden acts, due to the prohibition of khalwa (private seclusion) and looking at a non-mahram woman. You both must repent and feel remorse, not return to such acts, and separate. Increase in acts of obedience, perhaps Allah will accept your repentance, for He has promised to accept repentance. If you both wish to marry, then the young man should propose to you through your family.