Thank you for bringing your question to Just Answer!
Your reaction should be to be very careful in trusting this man. If he hasn't seen her since 2001, why would there be so much back and forth texting, and her worrying if he is "okay now?". Of course, he's going to tell you it means nothing--that doesn't mean you should believe it. The fact that he deleted all his responses shows he knows this isn't right, and he tried to remove the evidence.
Pull back, and make him prove his commitment to you before you get any more involved.
The fact that he accuses YOU of cheating is a huge red flag. Very often, when men have those fears and make senseless accusations, it's because he's actually doing what he's accusing you of...so he tries to deflect his guilt by putting it on you.