Regarding number one, I dunno. They're just points on the map that show that items that should have been there aren't there anymore. It's useful to the player, at least. If you think of the map as updated realtime, which if you have the map display in your possession like you do in Doom, it could be considered to be realtime.
If you prefer to think of it as a one-time update to your map computer, though, then you have to imagine that the map was probably made before you got on the level... but then why would it know where all the weapons and items were at that particular moment? What stopped the monsters from picking up the items before the player entered the level? It gets a bit existential if you consider this a bug.
Since no item can stack in this game, seeing those dots just reminds us that there was an item there. It helps the player, but not a lot, and doesn't really hinder gameplay. It sorta makes one feel a bit like a detective, figuring out where the monsters are by the traces they leave. If those little spots on the map were actually revealing terrain (meaning terrain that could affect the way the player plays the game) or something similar, that would be different.
Would everyone prefer that nothing be there? That if a monster picks something up before you get the map, that the map just shows what the current state is, and not what it was at the moment you entered the area? That might make the areas with multiple computer maps a bit more valuable, as you could check a new map to see if items were taken after you first scanned...