Could and might are often, but not always, interchangeable. He might have come / studied = 'We don’t know whether has come / studied or not', but you could substitute could. If you want to indicate ability or permission, however, you need He could have come / studied = ‘He had the ability to come / study.'
It's possible that he came from a different culture would be used in considering a historical figure who didn’t seem to fit into his environment. If you were talking about a current situation, you’d say It's possible that he comes from a different culture. It’s hard to think of any circumstances in which It's possible that he come from a different culture would be used, even if you regard ‘come’ as subjunctive.
English modal verbs are both important and subtle. You're unlikely to gain a full understanding of their use in exchanges such as this and if, as I assume, Noah, you are a non-native speaker of English you really need the help of a qualified English teacher.