Been away for a while and thought I would catch up! Dating sites - they are as bad as FB.
Snooping - we have all done it. Here's my take fwiw: Snooping can be a good thing especially at the beginning. I did not snoop until after BD, but wish I had done it sooner. It allowed him a chance to lie to me that much more. Snooping prevents gaslighting, especially when they are in that beginning phase. My xSO is still furious at me for going into his e-mail because of course that completely blew his cover - he was lying to everyone, including (especially me).
But now that you know, put it away. Take that fact for what it is - maybe he is just exploring. Assumptions get us into as much trouble sometimes, I think, than anything else: assume that he is unhappy, assume that he is happy...anytime we do not have the facts, we make them up. THAT does not serve us well at all.
Bright, I still think it is good that he is contacting you and being polite. And I think that you are doing well. Maybe step back just a little i.e. back to business again for a little while. Then, if he is responsive, slowly, slowly ease into more general conversation. We all want to go from 0 to 60 in four seconds, but that is not the way this works.