I'm thinking it might be a good idea to talk to him more about my concerns and maybe consider offering to try again after some time has passed, but I don't really know if it's a good idea or not because I never dated anyone with a needy behavior before. Needy, insecure behavior is fixable but it's not going to happen overnight.
You're not alone though..women are very turned off by needy men.
BUT that doesn't mean he gets to string you along while he does.
Rather than just agree to go along with the confusing "casual" status, maybe you should take a step back from the relationship and tell him to take some time to figure out what he wants.
You can tell him what you would and wouldn't be OK with—as in, "I'm fine with taking things slow, but I don't want to see other people" or whatever your bottom line is—and then give him some space to figure out if he wants that too.
I also the new person you're dating that you doubt she can measure up to the old one. He's clearly not over her, and that's my biggest concern here.
That said, I am sympathetic to the enduring trauma of getting over a long-term relationship.