My boyfriend is talking to a girl he used to love, and I don't know if I should be worried about it?

[A]

(OUR HISTORY AND WHY I BECAME NOSEY)
My boyfriend and I have been together for 10 months now. I knew him for 2 months before we started going out. He understands me like no other person, he likes me for me. He never lies to me. He will tell me the truth even if he knows it will end up making me mad at him. We talk about everything...except his old girlfriends. He want talk about anything to do with his ex-girlfriends (idk why). Just that he has had 4 past girlfriends. He recently told me that he has cheated before (and that bothered me because to me a cheater is a cheater)

(WHAT HAPPENED)
Well, the new paranoid me was going through my boyfriends phone and I started reading messages between him and a girl on Facebook. It turns out that she is an ex-girlfriend and she ended it with him about a year ago. She said that she didn't see a future with him(on facebook messages). They didn't talk anymore on Facebook until about a month before me and him started going out. She Messaged him having a casual conversation by catching up and then she randomly asked him “Did you love me?” and he responded by saying “of course…..” They didn't talk anymore after that. Then about 3 weeks later me and him started dating. We have been together for 10 months now. She randomly messaged him once or twice a month, for about the past 5 months saying “hi’ “hey” “hello” and he never said anything back. But now just recently (a couple of days ago while I was out of town) he responded back by having another casual conversation with her catching up. Nothing bad or anything. But now, knowing that he has cheated on girlfriends before, this makes me nerves, and I wont to talk to him about all of this but I don't want him to know and be mad that a was going through his phone/personal stuf.

(HOW I FEEL)
Him saying to her that he loved her hurt. Probably because he hasn't told me he loves me. Before all of this happened, and I read his messages, I thought I was falling hard for him and maybe in love with him (and I kinda thought he was falling for me) but now it all seems kinda sour. Before now I thought he was just a little nerves saying i love you to me/a girl, but now I know he isn't and idk what to think now.

(PLEASE HELP, I DON’T KNOW WHAT TO DO)
Should I confront him about it? if so how should I go about doing it?(I can never get him to talk about ex-girlfriends with me) Should I even be worried? Am I just a paranoid freak who doesn't give my boyfriend privacy and I should stay out of his phone? Or should I act liked I never saw it and keep on going through is phone with out him knowing it, and see if I catch him doing anything?(id rather not).. What should I do?…..

I would appreciate anyones input. Especially after you gave me your time by reading all this. idk how to make it a 3 sentence question. Any advice or opinions would be very much appreciated and helpful to me.