How should a young man deal with the first girl he was illicitly involved with, which led to family problems for her, especially after his repentance and remorse, and his consideration of marrying another girl?

The danger of romantic relationships between young men and women lies in their being an entry point for Satan and an enticement to sins. One should not be deceived by justifications like "innocent love" and similar excuses. You have done well by repenting, and you must be wary of anything that could draw you back into this forbidden relationship. As for the girl, if she committed sins by her own choice, then she has wronged herself, and you are not considered to have wronged her. If you strongly suspect that speaking with her father about marriage is a trick, then do not go to him. If you are asked about the relationship, you are not obligated to confess; rather, conceal your affairs and use allusions (ma'areedh).