Why didn’t Superman clean up the World Engine?
At that end of Man of Steel, Superman and General Swanwhick talked about convincing Washington of his trust, but it has to be on his own terms. There was a mutual partnership there. The World Engine was Government classified at that point and pretty much a crime scene. Lex had to have authorization from the Government itself to even step foot near the Kryptonian space craft, which was shown in the crooked operation Lex was cleverly orchestrating.
Since Superman didn't want to interfere with the Governments trust, he respected the authority and let the due diligence of America take its course.
As for "cleaning up the scout ship", even if Superman wanted to "clean it up" there was no way to breach the Kryptonian system. At the end of Man of Steel, General Zod overrode Jor El's conscience and the ship was overtaken by Zod's command. At that point, there was no way of entering the scout ship without a command key. Superman's command key was used in the operation at the end of Man of Steel to open back up the Phantom Zone. Kal wouldn't of had any control of the Kryptonian command for the technology to allow it to open up.
When Luthor was issued General Zods body, he used the Kryptonite to scalp the skin off of General Zod's hands; issuing him the necessary bio-metric identification needed to enter the Scout ship. From there, Luthor activated the braintrust of the ship.
"Team me." After that, he had ALL of the information he needed to override the system as his own: Alexandor Luthor, which allowed him to create Doomsday from Zod's body.
Why does Lex Luthor blow up the Senate hearing and kill his assistant?
Lex's entire point in the entire film was to frame Superman and make the people fear him. Walter was shown on television spray painting "FALSE GOD" on the statue and had an obsessive HATE for Superman for taking half of his life away from him and seeing his family perish in the Zod fight. On television, you hear Walter scream out as he was getting handcuffed that he was Bruce Wayne's employee.
Lex used Walter's depression and pain/ hatred for Superman to lore him to the Senate that day and promised him a new wheelchair; courtesy of LexCorp. Told Walter he can still live to stand for something. Bruce Wayne lost many employee's from Superman's fight with Zod, so Lex used Walter as a pawn to make it look like Bruce lost another employee because wherever Superman goes, innocent people die and in turn, made Bruce pissed off at Superman even more that he needed to be destroyed. Lex framed the country and the people into duping fear tactics against Superman and it worked.
Why is the Knightmare in this movie at all?
This is foreshadowing the coming of Darkseid. It's showing a post-Apokoliptic world where evil exists in the world. But at the time of Bruce's nightmare, he was dead keen on destroying and killing Superman. His hate for Superman was running wild, so instead of noticing the signs of Darkseid, the Omega Symbol and the Parademons, he dreampt of Superman soldiers as well and feared Superman would one day go rogue and turn evil. His dreams convinced him more that Superman was evil.
Flash's warning could of been telling him otherwise. He's breaking through the speedforce; timeline of Earth and coming back in time to warn Bruce. He mentions how he was too early and that Lois Lane is the key and to find the rest of them (Justice League.) Flash says he was right all along and to fear him and that he was always right about him. Bruce thinks Flash is talking about Superman because he's "too early" in the past, but he could be referencing Darkseid.
That's the beauty in that scene, which is the HEAVY debate right now. What is it referencing? Does Superman go rogue; ala Injustice? Does something happen to Lois Lane or is Flash trying to convince Bruce that Lois Lane is the key to not killing Superman?
I've already flip flopped on that idea about 5 times and can't seem to settle on what it's telling us; but it's referencing the future Justice League story set in the future.
Why does Superman stop Batman in the middle of clearly chasing bad guys and let the bad guys get away?
Superman simply doesn't know of what's going on with Lex's plan. Clark Kent is reporting and only focusing on the Bat vigilante in Gotham and is following Batman step by step. It's why Perry White gets on Clark's ass for not doing the jobs he gave him to report on at the Daily Planet. Clark is too busy following the Bat stories. For all Supes knows, those guys are no more than low level; worthless thugs that the crime scene in Gotham see's everyday and something that the Gotham Police Department can handle on their own. Supes is more worried about the torture and branding of these criminals and doesn't agree with Batman's torturing way of Justice.