Is marriage to a religious man 24 years her senior, after the girl has repented from the sins and transgressions she committed while studying abroad, unlawful or not, and does sin accrue to the parents for refusing this marriage for the same reason?

Sincere repentance is accepted no matter how numerous the sins. True repentance requires abandoning the sin, regretting it, and resolving not to return to it, in addition to increasing good deeds that erase evil ones. As for your parents refusing to marry you to someone whose religiosity and character you approve of, they should not do that. It is advised to try to persuade them, seeking help from those who have influence over them. If they persist in their refusal and there is a fear of falling into sin, the matter can be taken to a judge to arrange your marriage.