Well you said he will not commit to you so he is aloud to see other woman and if you are ok with that then you really can't be looking at his phone and who he chats with .

My advice is go date other guys , why be with just him if he is dating other woman ?
He sounds a bit controlling and it is up to you if that is what you want . If not then you need to let him go and find someone who shows you more respect and not put you down , how is that healthy ?