Yes, it is. The same guy leading the mercenaries, Anatoli Knyazev (KGBeast), was also the one conduction most of the operations in the US for Lex. The bullet Lois retrieved from the massacre was tested and found to be an experimental bullet never before seen. She went to consult the Calvin Swanwick, from MoS, who was now a Secretary of State. He told that the bullet came from Lex and that she'd have no support, and also that she needed to drop the case.
The small piece of kryptonite Lex owned came from the Scout Ship, that landed in Metropolis. The large rock of kryptonite came from the World Engine.
I explained that. Lexcorp found in Metropolis when the company was helping rebuild the city.
Batman's origin, which, yes, is a flashback, is shown in the contest of the movie as a nightmare. The same for the Metropolis attack. The nightmare with his dead mother and the huge bat monster and so on.
Because he stopped believing in himself and the mission. He couldn't help Robin, he couldn't change Gotham and he couldn't do a damn thing in Metropolis. The whole Batman thing was futile and only brought misery. That what Superman had done by bringing his war to the planet, was just like he had done before, but in a larger scale. That eventually things would get worse.
That's why he need to take Superman out, along with himself. He knew what he was attempting was a suicide.
See this vid.
I don't know. Sequel-bait.
The movie spells out that both city are across each other. Clark only has to take a ferret to go to Gotham. The movie also spells out that Gotham is a harbor city.
Because he could blame Wallace Keefer, the dude that lost his legs while working for the Wayne Enterprises branch in Metropolis during the Metropolis attack, and had days prior been arrested for vandalizing Superman's statue.
He would be able to take out the senator lady, create a huge news where more people are dead due to Superman's existence and this time inside US soil and blame everything in the actions of a poor sap that blamed Superman for all the bad shit in his life.
More bad press for Superman.
He had a lot of freedom there.
No, he wouldn't. Wallace would.