Search Results: not want to get back together

Here’s the gist. I’ve been dating someone for about 2 months, things have been alright but the other night we said I love you to each other, I initiated that but wasn’t expecting a reply of the same.
I have feelings for this person clearly but want to make sure that there’s nothing I should be worried about. So I did some digging (I’ve been hurt too many times in the past to not first dig around and see what’s up.).
First thing I find is their dating profile on the site we met is still active. Ok…not promising…
But then I found a profile of them and another person together like a joint profile explaining they were looking to hook up with a third and to contact them if interested.
The other thing I’ve noticed is, my significant other never asks me about my personal life or family, everything is surface. I’ve also noticed they do what I call parroting our conversations. So if I say something they say almost the identical thing back to me or will just ask me the same question I just asked them while trying to get to know them.
Break up or stay. What should I do?

Long story short, my ex didn't believe our daughter is his, dna test came back and proved it. We were still being respectful to each other during the whole time but barely talked since he didn't want to get involved until a dna test.

Now he wants to be involved which I appreciate for our daughter.

At 7 months pregnant I moved back home (from us to Europe) to support my daughter and make the best life possible for her having no support from him. I informed him about everything.

Its been almost 2 years since we broke up , saw each other and maybe talked like 5 or 6 times... until recently when the dna came back.

He wants to come out here and spend time with his daughter which I am actually happy that her father wants to be involved. We live in a one bedroom apartment and he wants to stay with us. I told him I would like him to get a Hotel room. we had barely any contact for 2 years I just dont feel comfortable with him staying here. He can spend as much time as he wants over here but I would appreciate him not to permanently stay and have a room to get back to. We never lived together and I just kinda like having our own little place for my daughter and I.

He got all mad at me saying he is already spending a lot on plane tickets and he can't afford a hotel as well. He says I would be keeping him from his daughter as he already lost so much time. I dont want to stand between them but dont want to compromise our safe space for a man I haven't seen in 2 years.