Is Affleck going to be Nolan-verse Bruce Wayne who somehow came out of retirement because JGL messed up?
No, its not the same 'verse. This was discussed at length when the film was announced.
Okay, so I'm gonna go ahead and be that guy: where was he during the Metropolis battle, then? He couldn't hop in a Bat-Plane and help out? And when Clark showed up at the military base, are we really supposed to believe no one mentioned that other cape-and-costume-wearing guy, or did those mentions just oh-so-conveniently happen off-screen?
He was busy. Major shit was going down in Gotham. (Same excuse they've used in comics for decades)
A bunch of people mentioned it, as you surmised, off camera.