Does this man really like/love me?

Just give it some time. If you don't want to get hurt, hold off on crossing certain boundaries that are extremely personal and tend to deepen the relationship for at least one person in it such as , meeting the parents, sharing painful history/secrets. All of these form deeper bonds. It sounds like he really likes you, but keep your friendship going and let your romance flow into the scenerio naturally. It iwll be more authentic.