Need opinions on these situations from my boyfriend?

After looking at the txt I discovered somethings and could use feedback.

1- him and his ex txted once while we were officially together. It was about a gym closing and nothing more. I was annoyed she was still there when hes told me the stuff shes done to him. He blocked her.

2- This girl who used to snapchat my bf whyle we were dating txted him asking if he had a girlfriend and he said yes. She clearly didn't care because she wanted to "shoot her shot" and have a date but, he said "my girl" makes me happy.

3- He loves to snapchat and senty some after shower snaps to this one girl. He doesn't send anything to revealing ever but its still the principal. She then had asked to come over and he always said "no its too late" but never said hey I have a girlfriend. But he has sent pics of us to her but she clearly didn't care. In the other txt I saw he said stuff like "drunk txting/calling again?, "somone at the airport looks like you" "im free next week maybe we can hang but I hate how pushy you are with the other stuff about cuddling and coming over"

That last one hurts but again he never said come over and has since blocked and we talked about this all weekend for better understanding and judgment on right and wrong.

Thoughts?