Is it normal that i allow my boyfriend to talk with his ex girlfriend?

I think if they are friends its fine, if its an Ex, then why cant they remain friends?
Don't think you are crazy, if you have feelings for him jealousy is normal. If it bothers you that much, you can always just ask him "why do you talk to her so much" and ask "would it bother you if I constantly talked to my ex and didn't allow you to read the conversations we have?" It will put it into the perspective from your side.

Do what you feel is roght for you. Usually your first feeling on something is the way to go
I hope every wprls out for you two.

Never date a guy that can't get over his Ex. He's immature and did not think to push her away in order to make room for your love.

PS4 and chill.

That word "allow" bothers me: how would you not allow it?

If you feel uneasy about it, tell him your feelings: VenomBurn's suggestions are good ones to follow

Eh, I'd say in some cases this is totally normal, but having conversations he doesn't allow you to read... That's sketchy. I mean, I also understand if he doesn't allow you to read them because it's his privacy, and relationships should be founded on trust... So you should trust each other...