You can be familiar with something or somebody. Something or someone you have seen frequently, and you recognize. You don't have to be intimate with a friend to be familiar with him/her. The word "family" comes from this same root word, so it's somebody you are comfortable with, or something you see often. It would NOT need to be a family member only, but a person you feel close to. It could be a neighbor, a school pal, or someone you have a relationship with. If you are not familiar with someone, you are not comfortable with them, don't know much about them, and you would feel an emotional distance between them. If you are not familiar with an object, you don't even know where it came from, and may not have seen it before now.

I do not know him (at all) or I do not know him well.

No, you can't use it in that way. If you're not familiar with someone, it means you don't know about him. It has nothing to do with friendship or acquaintance.

I don't think you can use "someone I'm not familiar with" to refer to someone who is not my intimate friend. The following is explanation of familiar (with somebody) from "oxford learners dictionaries" familiar (with somebody) (of a person's behaviour) very informal, sometimes in a way that is unpleasant You seem to be on very familiar terms with your tutor. After a few drinks her boss started getting too familiar for her liking.