Your husband is lying to you, plain and simple. Just because he doesn't have the tinder app on his phone does not mean he doesn't have an account. In fact, it would be quite easy for him to just download the app, log into his account, do his correspondence, then delete the app again. It also sounds like he's been doing quite a bit of trying out other apps as well. He is either doing his damndest to try and cheat, or he's actually doing it.
So, what to do? I would skip the confrontation. If he's been lying to you for this long, you'll never get the truth. I would just consult with a lawyer on this. Bring all the evidence, including the purchase history and everything. Get everything quietly arranged, and just drop it on him one day. He doesn't deserve a chance to defend himself, as he clearly doesn't respect you enough to just let you go and break things off. Trust me, he's already got a whole web of lies and cover stories ready.
So, what can you expect from him? He's going to try and mindfuck you. He's going to try and convince you that you're crazy, and that none of what you found is actually real. But no, things do not show up on your apple store purchases unless you download them. And no, him leaving his phone laying around would not make it susceptible to being hacked. He's playing you for a fool. And anyway, if his phone was hacked, or his iTunes account was, there would be a lot more mayhem going on. Lots of app downloads, money missing, information stolen, the whole bit. The odds that someone is going to hack a phone, create a dating site profile, go and crop photos, log into this account, and use it on a regular basis; that's pretty nil, and oddly specific. No, hackers don't do that kind of thing.
Your husband is a cheater. And it only takes 15 minutes to cheat. He could be meeting women at the gym, if he even goes to the gym. Heck, maybe you should have a friend he doesn't know create a tinder account, put the flirt on, and set up a meeting. When he agrees, surprise him with said divorce papers then. Sue for custody, and just take his money for child support.
And that's the best advice I can give.