Klaatu Barada Nikto? I have no idea what all of that means. I just thought Batman was having a vivid dream caused by watching Mad Max too many times, and mixed up by his fears about Superman.

The dirt rattling on his coffin pretty much confirms that.

I heard someone crying in the theater. I didn't think he was going to stay dead either, I think the point was to lay to rest any of the doubts the people IN the movie had about him and his commitment to the world & humanity. In the old movies, Superman got to run around being all altruistic and getting his brand out there long before Zod & company showed up. In this iteration, he was introduced as the good one among these aliens who suddenly invaded. His identity was first established as a Kryptonian, rather than as a person with powers from a Kryptonian heritage. It was the central fact of his identity rather than a background detail. Thus, Superman claims his humanity (while keeping the divinity debate alive) by making the ultimate commitment. The point of the death and funeral was to show that the world, or at least the country, had accepted his sacrifice for what it was. And it was a legitimate sacrifice, since he had no expectation of resurrection, which his farewell to Lois made clear.
I really want to give Ryan Reynolds another chance at Green Lantern after seeing Deadpool. I know they are completely different types of characters, but maybe with someone other than perpetual man-child Greg Berlanti running the show, it could be cool. IDK about the Martian, unless he was the guy who was Linda's boss on Supergirl, which I stopped watching after he gave his name as John Jones.
Irrational, but you're unfortunately correct in that it is plausible.
It's more like your neighbor who was minding his own business, happens to be walking past your house when enemies he did not know he had, fire rocket launchers past him to kill your family.

Pretty high if the typical resident is as stupid at Wayne's employees, who need Bruce to fly into town to call and tell them to clear out of a collapsing building.

IDK, this is a guy whose reaction to a pair of childhood traumas is to dress up as a monster and fight crime. He takes some pretty strange roads, to an extreme degree, on very little provocation. If he is going to declare war on crime because his parents got shot, eradicating the alien who was involved in the deaths of people who were under his protection is not a huge leap. As I said above, this is not the Superman who introduced himself as an altruistic vigilante & disaster-relief specialist, but rather an alien invader whose personal war caused a lot of collateral damage on our home. All it took for him to call it off was the recognition of Superman's humanity, which makes a lot of sense in that regard. Begging his murderer to save his mother changes him from an incomprehensible alien to a person in Batman's eyes. The fact that he was willing to suddenly help out the Kents proves, IMO, that he did not accord Clark that recognition before.
I think they were deliberately drawing parallels to the Joker. As I said in the original post, he's not as far off from Hackman and Spacey as you might think from the casting alone. He's closer to a typical Eisenberg performance, but Lex Luthor was not anywhere near a typical Spacey or Hackman role. Hackman's Luthor went around calling himself "the greatest criminal mind of our time" and both he and Spacey had utterly insane schemes involving the destruction of the American coast in order to gain a real estate monopoly, and expecting his ownership of the land to be upheld in the ensuing emergency situation. I don't think you could call either of them anything other than chaotically evil. Now, if the heroes were teaming up against a villain team-up, of the Joker & Luthor, that might be different, and you might want someone who could portray a colder, more rational version, such as one of the Gruber brothers from Die Hard, but one's dead and the other already had a role in this film. I can't recall off-hand any comic book movie villains who could be described as anything other than irrational lunatics.