Ok. I wrote a big ol' thing about this son of a bitch.
thecloneslegacy.tumblr.com/post/141988682878/batman-v-superman-dawn-of-confusing-thoughts
Read it or something.

If it's as good as Thor 2, Man of Steel or Avengers 2, I'm content with it (not totally satisfied masterpiece class tho).

Yeah, but their confrontation isn't a moral thing or whatever there's like 2 scenes where they face off, but the build up overall was weak, when the fight happens it's less a case of "They're on the same side but their clashing ideology doesn't let them realize that" like it should be, it came off more like "They are both retarded idiots that can't just say a few simple words to each other". Batman just turns on the bat signal and goes "Yeah. He'll come now."

What if Lex hadn't kidnapped Supermans mom and threatened to kill her with a flamethrower?

Would Batman just stand there until Superman came by? How long would he wait there until he figured Superman wasn't coming? Would he go home at that point and try again tomorrow? How many days would it take until Batman figured Superman doesn't want to fight him?

Why didn't Superman try to detect Lex's radio frequencies from his goons to find his mom? Why didn't he fly high up in the air and scan for her with his x-ray vision and super hearing? He had like 30 minutes to try this at least once. And Superman's faster than a speeding bullet. So I guarantee you he's faster than a Flamethrower.

Batman v Superman: Dawn of Contrivances.

It wasn't just about the people he kills, it was about Superman's potential to kill basically everyone. "If there's even a 1% chance that he's the enemy" etc. It's more of a "who watches the watchman" thing. Essentially Batman and Luthor are redundant in this movie.

I took Superman's stance to be more against the seeming cruelty/inhumane nature of Batman's antics, not the antics themselves. Dude brands people who then get horribly rekt in jail. And though the film is all dark and gritty, Superman's still supposed to be a more traditional good ol' boy.

I think something like a Red Hood film could explore this through juxtaposing BvS Batman with earlier Batman and using to delve into the relationship that that story line, in essence, explores. Because I'm pretty confident that this Batman, like you said, started off as the guy everyone knows him to be in the regular comic books/TAS. Otherwise there wouldn't any of his villains left, right? 

Maybe one of those criminals should have said their moms name was Martha. Then he probably wouldn't have murdered them via vehicular manslaughter.

I'll nitpick just a bit...

Batman doesn't know the people that are killed in the car chase. These are just hired guards - they could be anybody. They may not even know what they're transporting is illegal, just that they're working security, signed a non-disclosure agreement for work so they don't talk about it, and their standard operating procedure when transporting high value cargo is to do so as inconspicuously as possible, so they do so in plain clothes and at night. Hell, since people were killed they probably reported Batman's attack on the truck to the police afterwards.

The Batmobile tried to ram them first. That's the problem with attacking people with guns. They tend to shoot back.