try to build more experiences with him by spending time with him?
Yep. Ya did pretty good!
And get a better handle on not wanting to see his phone. Also, rehearse how/what you'll say, if anything (I'd say nothing at all, just accept it as a fact of life), when these unwanted phone calls come in. Probably best to say nothing. After all, that's his life right now. Gotta make the contacts 100% good times and nothing but.
The sex thing... I know some people say it can increase the bond... personally, I think that may be true for most women, but not most men. I'd suggest refrain from relations with him: he can't miss it from you if he's getting it from you.
And don't think about what he may be doing with her.