I don't think his mannerism's are fake, but after his arrest he can certainly be playing up his mental state. When Batman visits him, he's smiling it up when he claims "but who'd believe me, I've been deemed unfit for trial", as if it's a part of his plan. Which is why his expressions switches to "oh fuck" when Batman tells him he's been transferred to Arkham.
He could even claim that interacting with Zod's ship fried his brain
Anyone's expression would change to "oh fuck" upon being told they were being sent to arkham, regardless of whether it was the plan or not.
It's a fair assumption to make though. The guy has power and money, there's not much you can't do with those two elements.
See I find myself in agreement with Batman's actions, so I never really pondered the flip side. In my mind, Batman transferring Lex to Arkham ensures that he stays behind bars, something that can't be guaranteed by a jury
You're just assuming that he can get out, that he somehow holds influence because 'money and power' and I don't think that's reasonable. He's not a normal criminal.. With Lex's actions, he'll be the single most reviled criminal in America, someone who literally almost destroyed an entire city by unleashing the Kryptonian terrorist again except jacked up on super steroids and caused the death of what the entire nation now recognizes as a hero. The only way what your proposing works if we rely on really extreme comic book logic where prisons are made of cardboard and repeated offenders of mass murders are just allowed out willy nilly, something you'd think we'd be discouraged from in this 'realistic' version of of the DC universe. As it is, Luthor would be buried so deep in some random facility that superman would have difficulty getting in. He's also made contact with some wierd aliens of some kind while fiddling with the alien space craft. There is no WAY they wouldn't be monitoring him 24/7 just because of that alone.
And secondly, if that's true, then why not use his influence to send him to a secure facility that will treat him with compassion like the people of metropolis/gotham want? Instead, he sends him to Arkham, the hell hole facility of a hell hole city, taunting him specifically that he will not be treated well there.
Either way, he's basically looking at society and going "...nah, I know better than you idiots" and violating society's rights to do as he thinks best. It's the kind of misanthropic, benevolent fascism that permeates Frank Miller's work. Batman 'knows better', so he has the right to do what he wants.
I wouldn't go that far. I could see how many here will decry Batman's actions, but my normie friends (and I use that term jokingly), loved the hell out of Affleck's Batman. Hell even in many negative reviews for the film, Batman is considered the high point.
Because Afleck is a good actor and he brings the character to life with his talent. In many ways, this batman is the best performed Batman. He's just utterly revolting. People cheer at the action choreography and the grimdark 'badassery' because he kills people and that's dark and therefore cool. But if you don't put a positive spin on things, he's just a fucking monster. A sadistic psychopath on a power trip. The movie doesn't give you a reason to think that Lex Luthor has any influence after he's caught. It might be plausible to infer that he might, sure, but it doesn't actually
give you those things. So if you go by the movie itself, and not make up any excuses for Batman's benefit, you realizes that he has none. He's just an evil and vile person.
And if you still like that, whatever. No moral judgements on you. Sometimes, it's just interesting to look at the ugliness of humanity. Tarentino is really good at making those kinds of narratives compelling, I love his films. But he's a phenomonal director. Snyder....isn't. The darkness that Snyder pushes on the audience is oppressive enough, but this is also such a badly made film on top of it. There probably is a way to make an evil batman interesting, butt this wasn't it. I've gone over many times now how it's a movie that utterly fails narratively, regardless of personal like of Batman himself and can link you those if you want.
So all I'm personally left with is a Batman that's badly written as a character and just bad as a person. If you enjoyed the movie, cool, and I think I understand what you see in it and can even sympathize with that....but make a mountain out of a molehill. He's not a deep or well written character. He's just fucking deranged. If that's fun to watch for you, cool, it's just...not something I think is healthy to overly endorse or not reflect on.