Is the marriage that took place between the young man and his maternal uncle's daughter, which included offer and acceptance and the giving of dowry, considered a legally valid marriage, and is she truly his wife, knowing that both were mature and of sound mind?

Exchanging love with a foreign woman is a reprehensible act and a means to corruption. No marriage is contracted by saying, "I marry myself to you." Attempting to influence her does not justify the forbidden relationship; rather, it is one of Satan's stratagems. You must repent and sever the relationship immediately, for the woman is a stranger (non-mahram (definition)) before the marriage contract. Finally, Abu Hanifa does not validate marriage in this manner, but he permits it without a guardian (wali) if the other pillars (arkaan) are fulfilled.