He presumably means he will only indulge in sex exploration - sending texts, looking at websites, with Daisy present.
Daisy, I have read this whole thread over again (I have been reading since the beginning), and I have now looked at your other threads.
I think there is a completely innocent explanation for this and you are unpicking your life on the basis of the advice of people you don't know and who don't know you or your DP.
When you found the messages fom the porn sites, could you see that he had actively and recently added his details? Because any man who has ever dabbbled in looking at porn sites (and that's most of them) can tell you that once you have looked or joined up to one, you will be plagued for ages afterwards by extremely dodgy emails from woen advertising themselves, and that your details get shunted fom one site ot another - Data Protection isn't a feature of these small seedy, highly mobile sites. He could EASILY have been receiving this kind of spam from his former adventures.
Perfectly ordinary men also look at these sites out of curiosity.
The phone thing - well he was clearly fantasising about you, hardly the most awful crime, and sent the texts from his phone to his phone.
He stopped seeing his dodgy mates, he has bought a new cooker, you talk again and again about how good he is with your kids.
I just don't recognise this abusive, scheming, lying, gaslighting, blackmailing, deviant emotionally abusive pervert that has been purported on this thread.
Just tell him everything you found, how it made you feel, and talk to him, instead of talking about him with people who know neither of you.
I don't know how he can 'prove his innocence' of a crime you don't even know exists. He wants to talk about it but again you are declining to talk openly and fully with him.
I really hope it all works out.