First of all ,No, you shouldn' t all boys and men brag. Have you had sex with your ex? If, yes, what makes you think he doesn' t know about it.Besides you don' t know what going to happen in the future with your ex boyfriend. Especially if your young.Just wait and see if he'll stay around without you have sex. What's the rush? Hopefully he is not using you.Sorry to say but that's the way it is.
It is your choice. If you like him that much then I guess so. Since you don't have anymore connections with your ex, then it doesn't matter what he thinks.
No! That is the unwritten rule. You will end up causing bad feelings between the 2. Even if you have a reason to resent the X, that is just considered bad form, and you could loose a lot of respect for yourself, and from others. Years from now, if your ex and this guy are not so close, you may reconsider it, as it may do little damage then, but for now, I would abide by the social mores and leave it alone.
I say treat others the way you would want to be treated. Would you mind at all if your ex had sex with your best friend? And guys can't keep secrets, it would come out some time or another. Don't burn bridges, always stay on everyone's good side.
I would say that he is an ex therefore has no claims to you or anyone else. If you want to keep it on the down low then there are other issues why you shouldn't. If it can't be open then you shouldn't do it.