You sound very insecure. We can’t help what we feel, so if you feel a surge of jealousy come on, that’s fine, but that doesn’t mean you should act on the jealousy. Asking him to wait outside was uncalled for. Both looking an ex up online or even talking about them could be within the realm of normal, but I think that’d depend on the frequency of the behavior. Also, not everyone snoops — I have never.
I would’ve happily stayed with the guy I dated from 26-28 if he hadn’t cheated one me. But, he did cheat on me! That changed everything! I’m years removed from that now and it can still feel sad that our relationship ended how it did, but I have no regrets that we’re not together anymore. I doubt your boyfriend thinks of his cheating ex-girlfriend from five years ago as the one who got away.
Take the energy you spend focusing on your boyfriend’s ex’s age, fitness, and beauty and use it to do the things in life that make you feel healthy, beautiful, and confident.