I wouldn't recommend adding salt. Lights off for a day isn't a bad idea; lets 'em relax a little. when you do go to light up their area, let some ambient light or indirect light happen before you turn the one directly above them on. Sometimes discus, especially new, nervous ones, will spook when an overhead light is turned on when the tank is completely dark. They can hurt themselves badly when that happens.
As for the two laying on their side... I've seen newly shipped discus do that. Give 'em time, they'll likely be fine.
Remember, they're in a new, scary place. You're a big, scary monster. They may hide when you come to the tank. Again, give 'em time to get used to their new home.
When you feed, and new babies need to be fed often, you may have to drop the food in, then walk out of the room. You can peek around the corner to make sure they're eating and see which one(s) (hopefully not in your group) are not.
Once they get comfy with you and the new home, you can train them to eat out of your hand.
Once the pecking order games start, watch out for the omega hiding all the time and not getting any food. They'll usually stunt if they get picked on and hide too much.
I would definitely rehome the BRs and otos for the reasons Paul already gave you.
Welcome to the world of disus...one of the coolest fish ever.
Mark