So sorry you are going through this. Your head must be a mess right now. And your poor DD too.
He only finished the affair when he was found out. thatis, if he has actually finished it, which I very much doubt right now. Remember this. He isn't sorry for risking hurting you. He is sorry he has been caught. His tears are only for himself.
But you need to be prepared. He has already started 'the script' if you are unaware it goes something like this.
On being found out and confronted with evidence he will confess only to the absolute minimum. This generally will be only confessing to the stuff he knows you know.
He will look as though hes remorseful, he'll say how stupid he was, he'll try and minimise any feeling for the OW to you, he will cry, he will beg, he will tell you he loves you more than anything. He will likely swear on a childs life too at this point.
But there is far far more to it than what he will initially confess to, and you have to be prepared for stuff to start drip feeding out.
The next stage will still be denial, but he will admit to the other little bits you discover. This will continue until you have discovered so much he cannot deny the whole full blown affair.
Once this is done, he will start to blame you. He will rewrite history. make it your fault he strayed. He wasn't happy (news to you, I bet), you didn't understand him, this may well turn into him saying he never wanted to marry you in the first place. He will justify his affair any way he can, making himself the victim.
There may then be an anger stage. How dare you be upset when it was all your fault in the first place. He might add more tears and may even threaten to kill himself.
OP, you know deep down he has had a physical affair. No man sends gifts and love notes like that to someone they are not sleeping with. But the main thing is that he has looked you in the eye everyday that that affair has been going on. What kind of person can do that? You will never be able to trust a word he says again. Never be able to not worry where he is, who he is with.
There is lots more to come out if you choose to look. If he genuinely was not having a physical affair, he would be able to show you messages between them, bank statements, anything to reassure you. If he does not go all out making sure you have access to this stuff then you have your answer anyway.
Personally to me it wouldn't make a difference if he had slept with her or not, he'd be out the door.Immediately. Based even on just one of those messages you have shown. But I think like you, I'd still want to know.