How can a non-Sunni girl marry a Sunni young man and convert to the Sunni madhhab, taking into account the potential harm from her family, and what are the Sharia and legal procedures for that?

Marriage is the best guidance for those who are in love. If the woman is an adult of sound mind, she has the right to marry herself and cannot be forced to marry someone she does not desire. A virgin should be asked for her consent, and her silence is her consent. However, a guardian (wali) is essential for marriage. If the guardian refuses to marry off his ward, or if she has no guardian, then the ruler is the guardian of whoever has no guardian. Therefore, she should refer the matter to the Sharia court.