Search Results: should i add her on facebook

So I've been dating this guy for about 1 month now
He has been treating me right so far - taking me out to dates often during the week, holding my hand, showing affections in public, etc
We made it official last week
He told me about his past relationships:
- his 1st girlfriend lasted more than 1 year and cheated on him and he said he hasn't talked to her since they broke up 10 months ago
- his 2nd girlfriend lasted few months

So anyway, I was stalking his facebook and i came across a post from last year
It was this girl with his family
I clicked on her profile
And her cover photo is a picture of the guy im dating and her
And then i scrolled down and she's been posting stuff for the guy that im dating
Its saying that she still loves him through their ups and downs
This post was 2 months ago
And posting pictures and videos of them both
But it says on her profile that she's "single"
And it says that they were meeting up on valentines day (which was 3 months ago)

I confronted him about this and he says
"Thats my first girlfriend.. Im telling u the truth.. i haven't seen her since we broke up.. we dnt talk anymore"
But I dont entirely believe this because it doesn't add up
So i told him that im going to message her to find the truth
Its weird that his ex girlfriend still post about him and has a picture of them on her cover photo right?
They dont have each other on facebook though (theyre not facebook friends)

Should I message her?
Or trust him?

I've been seeing this guy recently
We had few dates already
We met on a dating app
he's seems like a nice guy and such a gentleman, and quite fun to be with
He has been bringing up this after the second date:
- He asked me if I wanted something serious
- He said he wants this to go somewhere and asking if Im on the same page as him
- He asked if my parents would like him
- He asked if I care about his background
- He keeps saying he likes me a lot
- He asked me how I see myself in 5 years
etc
He always wants to see me often
After our 4th date, when we were kissing, he said:
"I really like you alot"
And then he asked me:
"Can we be more than friends? I want you to be my girl"
But I replied:
"I think I need more time, I don't want to rush anything, I just wanna hang out more and see where it goes"
Then he replied:
"Yeah sure, I understand"
And then I asked him:
"Are you still on the dating app?"
And he replied:
"Nah why?"
And I said:
"Just asking"
I deleted my profile few days ago because I am so over the app
Most of the guys are just douchebags that just want to hook up
So I didn't want to go on it again
But I went on it again to see if he's recently been online
And he was online few hours ago
I have him on facebook and his friends list is on public so I can see whether he adds new girls or not and he hasn't
But should I be upset about him still being on the app?