For your second point, I believe there are only two ways to have children in their world and they're both very well known just one of them is just forbidden. I think that's why he knew immediately what she was talking about.
For your third point, I think in their world it is still natural and at least some people still get urges. So, when he tried it he realized he liked it and wanted more of it. While she was just embarrassed by his forwardness because she wasn't expecting it. I mean there are times he even does it in front of people.
For your finally point, I think it just depends on the person for how easily previous held beliefs can crumble and with his reaction to his parents I don't think he was all that brainwashed by what was being forced on him. Heck he was willing to give up his country for his wife.
I disagree totally on the 3rd point. Its purely shoujo/josei purity culture bs where the FL always must be the innocent one even when she's more experienced/worldly and the ML is somehow always skilled and knows how to guide (see: push) FL into a new level of "indecency". Most people like sex but just bc they try it and like it doesn't mean they are automatically comfortable, knowledgable and very forward.
The rest is also just fiction stuff. He gave up his beliefs for love because its fiction. A level of brainwashing like that wouldn't be overcome that easily in reality. My points are the author's thinking is very shallow lol
I see were you are coming from on your third point.
In reality "brainwashing" is a very complicated matter and some people don't need much to leave the life they were raised in while others do. That's what it was like for me. I'm the second oldest and I was raised in a family that had terrible beliefs and it didn't take hardly anything for me to turn around and say this way of life is unacceptable while my brother's either still accept it or are struggling to unlearn what they were raised to believe. All it took for me was, while I was in my teens, seeing that others were harmed by those beliefs. While for my brother's, who have started to change, even with seeing those things it has been harder for them. Some people can easily change from indoctrination and "brainwashing" while others find it near impossible, it depends on the individual case. I wasn't saying everybody does in my comment I just meant it was possible for him to do that. But you are right on it not mattering because no matter what the author can write whatever they want whether it makes sense or not because it's fiction.

This premise is so strange.
Firstly its impossible to stop two heterosexual adults from touching and having sex when they have considerable privacy and sleep in the same bed, even irl there are religions and circumstances where meeting the opposite sex privately is taboo and even illegal yet people still do it. I mean even teenagers or preteens have sex despite the constant barrage of forbiddance.
Secondly, if even holding hands isnt allowed, how did ML immediately know what the FL was talking about when she alluded to making a baby with another method?
Thirdly, the ML is illogically smooth and good at physical touch and FL is from the real world where physical touch is totally normal yet shes the one being pulled along and shy. Would make more sense if ML was the reincarnator if the author is going to insist upon sticking to the strict shoujo gender roles
Lastly ML as a prince should have had the most conservative upbringing of anyone in his world but showed almost no resistance to breaking what would essentially be a lifetime of brainwashing and indoctrination.
And ik it aint that deep lol