What is the ruling on marrying the aforementioned young man, and what is the interpretation of the dream for a woman who committed adultery and repented, fearing exposure?

We have no knowledge of dream interpretation. You must repent to Allah Almighty for the immoral act by abandoning it, regretting it, and resolving never to return to it, while keeping it secret. If the man repents, there is no impediment to your marriage, but be cautious not to be lenient with him before the marriage contract, for a suitor is a stranger [non-mahram (definition)].