Joker has people all over the city. It is possible he hid the bombs, it is also possible the place was rigged long ago he just felt now was the time to trigger it. Explaning this would be like trying to figure how Batman dissapears all of a sudden.
The goon with the bomb in his stomach was a crazy person probably from Arkham. Joker promised to get rid of the voices in his head if he put these "lights" into his stomach.
Joker probably didn't plan on being arrested, however he probably planned ahead if he was to get arrested. The man with the bomb in his stomach was his back up plan. He could use him for any situation, his use wasn't simply for breaking out of jail. It is his ace up his sleeve.