Not really. Trauma is different for each people. Adult has their own difficulties too.
And yes, he is aware. The emperor himself said how can not recognize the face of whose child he was with.
And no, you're wrong. He's sincerely feeling apologetic and bad for saying that to her. Not like he abused her physically. Except for saying shit to fl, the wrong things he did only based on that book. I don't understand why he's unredeemable.
I just want to correct you for he awareness part. He did not know she looked like Kathrine until she revealed herself. You repeated the exact phrase that told us he never caught on the fact that she looked like someone else, so this cannot be used as an excuse like Scarlet Angel stated (the OG comment). For the rest of your statement I have nothing to say
Him feeling apologetic doesn't change what he did and it's upto her to decide whether she wants to accept that apology or not since she was the victim
And yes people have different trauma and it affects them on different basis but that doesn't justify their actions against people who have done nothing to them
And abuse is abuse be it emotional or physical
Just because he didn't physically hurt her doesn't mean he didn't abuse her
And child neglect is one of the most common form of child abuse
I know the emperor committed mistakes to FL but note that, she is the mini version of someone who told the emperor to take her as his concubine. Plus he lost his wife and he was mentally unstable at that time. The emperor is redeemable character if you ask me and it's not the execution happened in real life. It was from the book which the FL become suspicious of as time goes by.