YESSSSS!

If someone is so utterly insecure with themselves that they can't appreciate the love you've felt in the past, then they need to learn to love themselves and get over it. I believe in the philosophy of enjoying yourself enough to not be too worried about such trivial matters. There are many bigger things to lose sleep over.
I personally hate being repressed in any way, and I encourage my lovers to tell me about all their past girls and whatnot. I'm curious and not a jealous person at all. I'm always intrigued as to know what kind of people they were interested in, and why, why they stopped seeing each other, etc.

If you mention the immediate ex constantly, or bring them up incessantly, it is not okay, that is rather excessive and not terribly fair to your other.
I think you should have him approach things from a more confident view, as reassuring someone constantly is draining and annoying to you, and it takes a great deal of energy, too.

Oooooh. I wish I thought of the "good cop, bad cop" interwebs interrogation technique first.

I never know what to say about myself. I always am told that I am some variety of an enigma. Being unintentionally weird seems to keep that sort of empty banter to a minimum and filters potential boredom out automatically. Let's write a book about it!