
I feel like he's already aware of this as those are personality traits from even before his arrived at Noart.
So, I think it's less that he believes the lady is totally good and/or truthful. More that if there is a kid and it is his, he'll do what he feels is his duty immediately and halt any questions or self doubt about the situation.
Just my 2 cents

Yeah, I do not recall what chapter it is, but he does say that he must NOT ever doubt the child is his. Even if everyone else does, just the possibility of the child being his means he must never doubt his own child because he would never forgive himself.
It is less about believing the woman, and more about protecting his (possible) child and sticking to his principles.
I also think he might distrust his adult self, and I don't blame him. Imagine being a teenager (full of rage, as the manhwa says ) and you wake up one day, and you are the heir to a fortune and people around you say you are an adult who has his shit together.
He doesn't know who he was, and his sister insisting it is not possible is not going to change that. For him, waiting for the "child" to be born and having others check for the paternity might be the best solution.
Why didn’t Mc just tell her brother that the child couldn’t possibly be his bc he never mentioned nor talked about having a lover or anything. Also he basically told her before he lost his memories that he’ll never marry/have kids unless it’s within a political marriage that will benefit him which Mc knew that him saying that implied that he doesn’t have any lovers. Why can’t Mc just tell him or explain that or am I missing something that’s preventing her to do so? I’m still only at ch 31 so maybe I’m missing soemthing ╮( ̄▽ ̄)╭