A month ago, she finally had to give in and let him see his kid. He started communicating with her again.
also one of the things that is very logical to me and i think it's alright.
Well it would be alright if my boyfriend didn't start making problems himself in a way. He recently told me he has to keep her sweet so she lets him see his child and i understand that.

But he started saying lately he is very worried how it all looks like and he doesn't trust himself with her. Because before he would be in a relationship and be friends with hsi ex and end up back together in a way sleeping with each other (it's how he got a child). He started talking about how they were talking for 2 and a half hours on the phone and he told her about how he doesn't trust himself and how he feels he is being unfaithful to me by talking to her. So they started talking how they don't wanna make the same mistake again and ruin their current relationships. And she is actually kinda trying to sleep with him again and she is inviting him to his house at night and stuff like that (he never goes cuz he wants her on distance). He is giving out a lot of information to her about how he feels and some info what are our plans for these few months and kinda it's a talk about our relationship.

All it would be fine if he didn't say "i don't trust myself". It kinda feels like their two are making an agreement to be fair to their relationships and he maybe is being honest, but she is kinda trying to sleep with him cuz he is his safety net. And he is not exactly giving her exactly clear cut on this. By saying things he does, sends her a message that she could spin him easily.
I don't think he will really cheat on me with her, but i know my boyfriend is not too strong person and he could let her sneak into our private life. In my opinion talks with her on that kind of personal level, while knowing she is actually trying to sleep with him, are not very welcome.
I told him all this and he said he can't help but not to talk back when she talks. Like things are not in his power.
I'm a bit worried for his lack of character.

I don't know what does he means by not trusting himself exactly. I think he is scared of the contact with her and her. I told him i understand his fears and that getting rid of fears is by taking a situation in your hands.
That's all i could think of.

Any advice, comments on my situation?

i don't know what to say. But i kinda don't want break up before seeing what's happening. I gave him a warning and told him what i think and he said he agrees with me and he should grow a pair.
But i did think what you have just said. Weak character is not a good thing for anything and he is rather weak when it comes to standing up to people. And as you said, sex with an ex is not my concern exactly, but these other things you mention and him saying he doesn't have a control when he does. And i did tell him that and as i said he answered he needs to grow a pair. And he said himself he feels exhausted and fear that he is gonna loose me and his daughter again in a period of few months.
I will be honest, for someone for who i am rather sure that loves me...he is not thinking of what he is saying. Talk of 2 and a half hour is an alarm and he called me after that and told me he feels bad about he talked for so long with her. And when it old him not to give out that much of information he told me "as you said...i can't help but talk with her when she talks". That tells me he is either scared of her or didn't get over it.
His ex did a lot of crap to him. They had 5 years of on-off relationship which ended up pretty badly. She broke off their engagement over text on Valentines day, she was texting him after break up to let him know she slept with someone else, and later when he would find someone else she would show up at his door to try and win him back. Later on they got a child, she accused him of domestic violence that never happened and put him 5000 pounds into debt cuz he had to go court to see his kid again.
So with saying that kind of amount of bad things happen to him caused by her...you are right, he is maybe emotional about her but more in a negative way maybe.
But tell me your opinion - you think he is emotionally into his ex? In what way?

the thing you said about him not being emotionally over his ex...that is my fear. Because he is constantly repeating i am only thing he wants in the world but these kinda of actions with 2 and a half hours on the phone shows kind of lack of respect towards me. And i fear that there is smth unresolved about his ex and that he is maybe in some way still emotionally into her, as you said. I wouldn't say it's romantically necessarily but it could be any other kind of emotional connection.
And i am worried im gonna make a wrong judgment here. That if i do believe that he is emotionally over her that his actions will show he is scared of her or that he can't be firm.
But he has also general issue with being firm with people.
I'm thinking many things here. And i am not sure how to behave in this situation.
I'm said to him i don't want her in our private life and he agreed. But i don't want her in his private life either which is the thing im scared it's gonna happen.
It's very tricky for me to say what is exactly happening.
I understand he is scared because the judge didn't make contract about him seeing his child so he is again on her mercy will she let him see her or not. That could be his biggest fear.

agreed. It wasn't some formal call. She often calls him to say goodnight over phone to his daughter and then starts chatting him up. Plus she is inviting him to come down his house. And with that she has kinda free road because we are on long distance. I'm not there next to him so she feels like she can pop out or call him whenever.

See, this is something that puzzles me, even though I've done it myself:

We blame the other person & not our partner/boyfriend/spouse.

*She* isn't the one who supposedly has a partnership-type relationship with you.

*He* is.

*He* talks to her for 2+ hours at a time, etc.

*He* makes excuses to you & keeps on talking to *his* (supposed) ex.

Throw this one back & leave him in the past.

You have your own life to live, & you'll live it better without his (her/their) sordid melodrama.

I wish you the best.

nah, i don't blame her...im aware of her intentions.
but it is his blame he doesn't put a stop on it.

so yeah...im thinking about is his "melodrama" worth it. Not only because of his ex...that's the least. But generally strenghtless, can't admit mistake, stubborn and depressed is not maybe a way to go. But that's if im cold headed.

I'll see for awhile how things turned out. What he will do, how will all this function. But he did admit he made a mistake with the phone call and told me he will put her in her place. If it does happen I'll be happy. If not, I won't be very happy.