2. It's related to the Kryptonian ship because he clearly didn't trust the government (hence him destroying the drone) so why leave the last vestige of his heritage LAYING IN THE MIDDLE OF THE CITY.
You're inventing something, that isn't there. He didn't want the government to know where he "hangs his cape", that's all. He doesn't want to be spied on. Kryptonian ship has nothing to do with it.
3. I have no problem with Batman being tricked, but how was he tricked? His issue with Superman had to do with a lack of research, not anything Luthor did (and really what did he do? Send him some scrawled on checks? Really...). At least with Bane/Catwoman/Talia you could make the arguement that he was rusty from being out of action for years, with the Joker he was at least using detective work and Ra's was the mentor tricking the mentee, but Luthor did NOTHING to sway him to fight Superman. Less than nothing actually.
Alright, it probably doesn't convince you. Whatever, different strokes... But I felt it was a really nicely constructed arc for Batman. Deep personal crisis due to lack of progress in his crusade, feeling of powerlessness and guilt, that had deep roots since murder of his parents, then death of his employees and crippling of Keefe. Keefe also blames Superman. He doesn't receive money from Bruce, because Lex intercepted it. I like how those scrawled checks fueled guilt and rage of Bruce. At the same time, he wanted to deal with Superman on his own, Lex just stimulated Bruce's emotional state just a tiny bit. So yeah, I buy his lack of sense due to his emotional condition.
4. Lies for you. They were blaming the deaths on Superman, not other people killing because of Superman, hence why Lois was investigating the bullet and giving it to the General to clear Superman's name.
Blaming the deaths on Superman isn't the same as thinking he killed everyone. Superman goes to another country, does something, that leads to mass bloodshed, according to the witness. There's no details about what happened exactly.
5. Once again, you are not explaining what Wonder Woman's actual purpose was in THIS movie outside of "come in at the end and fight Doomsday". She served no purpose but to set up the Justice League movie. She was essentially "Hawkeye in Thor".
Ultimately, all major characters go through crisis - Lex, Bruce, Diana and Clark. Superman ties them all together. I believe, they choose the wrong title for the film. Because it's not about conflict between Batman and Superman.