The movie is a (direct?) sequel to Superman: Doomsday.For two things I can think of:
1) Clark and Lois are married and she knows Clark is Superman. 2) There are robots operating at the Fortress of Solitude. He had one in Superman: Doomsday, so he might have made more and with different designs by the time of Superman vs. the Elite. He might have gave the original robot a new body as well, and he was the one who flew Lois to England and back to Metropolis.
The whole time, The Joker was in Arkham, watching the news reports of it and laughing his ass offWhy? The public was supporting the Elite's lethal methods. The way Joker saw it, this just proved that he had been right about everyone else being no better than he was.