"Man of Steel" sequel plot holes

The "Man of Steel" actually seemed like a better movie the second time I saw it on the big screen.
However, there are some plot holes that could resurface in a future sequel to the movie.
1. Although I did see a LexCorp name on a tanker trunk in the movie, Lex himself was nowhere to be seen.
I find it highly out of character that Luthor, a genius, would do nothing in the "Man of Steel" movie while Metropolis was invaded by aliens.
The movie could have easily referenced Luthor, without showing his face, as having a backup plan of his own, if the military and Superman failed in their efforts to stop Zod.
2. Jimmy Olsen was nowhere in the movie. Why?
That Jenny Jurwich character at the Daily Planet was annoying, though -- more so than Lombard. (Also, I'm still 
trying to figure how Clark Kent got a job at the Planet. 
Nowhere in the movie were any journalistic leanings or training mentioned for Clark ....)
3. What happened to any Kryptonian tech/ships leftover from Zod's attack? Did Superman salvage anything, or did 
the government get it?
4. Why wasn't Superman's actual landing and being found by the Kents shown in the movie? Will that be some bonus 
material in the DVD?
5. The fact that Lois Lane knows who Clark Kent is from the onset dramatically changes their future relationship.