Is a young man's talking to a young woman and promising her marriage (engagement) considered unlawful, especially given that he has stopped watching forbidden things and is a person with special needs? And is this a gift or a test from Allah?

Speaking with a non-mahram woman is not permissible except out of necessity and while adhering to the Sharia guidelines. Therefore, one must fear Allah and be patient until marriage takes place. If marriage does not occur, then the relationship with her must be severed, and one should ask Allah to replace her with someone better.