I think the whole grooming/CSA allegations are a pointless rabbit hole to go down right now. Even if you could prove the emails are real (as in an actual email) it doesn't mean anything
Unless you can prove that the email existed, that he was definitely the person in control of the email address and that the messages were definitely posted, then it's impossible to prove they are legit.
All you might be able to prove from the screenshots themselves is whether they were definitely faked, such as if the font used wasn't released until a later date. And just because they might use a valid font for the dates, doesn't mean that is evidence that they are real. i.e. you can likely only prove the negative from the images themselves.
Even though the messages appear to fit with other known facts such as his wife finding out about him "texting girls", and would explain the still bizarre "I'm not going to record the judicial meeting because I have nothing to hide" claim, that would still just be circumstantial at best.
But we do know he uses prostitutes in countries with CSA / trafficking problems, which is why the accusations are useful to him as a way to label all claims as false and vindictive lies.
It doesn't need to be true for the rest of his behavior to be despicable.