What is the ruling on marrying a girl who had previous relationships and possesses pictures and videos showing kisses, despite her claiming repentance and forgetting about those pictures and videos?

Every human being is susceptible to sin, and what is important is to repent afterward. If the woman repents and you are reasonably certain of the sincerity of her repentance and her steadfastness, then maintain your engagement to her and marry her. However, if she does not repent, or you doubt the sincerity of her repentance, then seek someone else. As for the pictures and videos, you can discuss with the man the possibility of removing them.