What is the correct breakup behaviour?

my ex texts me now and then and puuts a kiss on some of his messages, he asks aabout my nite out, hes even text at 2 in morn to say goodnite,and when there was rumour of him seeing someone he made sure to tellme that there was nothing going on. even today id made a comment about not wanting to pry into his personal life and he said he doesnt mind.he left me and i find this rather odd beaviour.its too raw for me to be his frind we were together 7 year and have children.my friends and family say that it appears he wants to come back but im pretty sure that is not the case so what the hel is going on.i feel like i cant move on