Check behind objects in rooms... I "lost" mine too at some point, but it was behind the bar of my lounge room.... Same goes for other rooms of course, especially the upgraded ones because they become much deeper on upgrading.....
To find it, zoom fully in and drag the camera left/right/up/down per room. See if you can watch "around corners" that way to see if it's lying there.
Be quick, because after 24 hours it should get deleted..
Probably... sorry to hear that. I think they tell you the first time a dweller dies doesn't it? Maybe they just assumed that everybody would just ... know?