Is it obligatory for a man to marry a girl with whom he had a relationship that included impermissible acts, knowing that he does not see her as the suitable wife and that he has repented to Allah, but he still checks her social media accounts?

The Sharia came with warnings against the temptation of women, and whoever violates this falls prey to Satan and his seduction, as in His (Allah's) saying: "O you who have believed, do not follow the footsteps of Satan." Talking to women unnecessarily is sinful. You have done well by repenting, and you must follow the path of righteousness. There is no harm in accessing the girl's account with her permission, as long as it does not lead to anything forbidden. However, there is a fear that it might be a pretext for unlawful communication, so be careful. If you desire marriage, then seek a woman of religion and good character.