I don't find his behavior particularly strange, but I would stop the move-in-with thoughts; if he's going to have his own place, etc. then you want to spend time with him, at his place nearly as much as he spends with you at yours. Don't let him use you (to get away from people who are looking for him that he doesn't want to know where he is?).

If he has associations with shady people and you know he does a lot of talking with other women, I would rethink how much I'd like to be involved with him; what's the future prospect of happiness look like?

Don't question his actions, decide on your own and let him know. If the behavior is unsettling to you, that is how you feel and he cannot argue with that (he can try, but it's how you feel which he has no control over :-) Let him know you don't need his protection, you are perfectly able to care for yourself but don't need people around you that think you need protecting! Agree with him you feel insecure! There is nothing wrong with any feeling you have, it isn't coming out of thin air.

Tell him if he associates with shady people he does not want to bring to your home (don't do "our") that makes him a shady person also and you do not wish to associate with shady people, never mind who he wants you to/not to associate with.