The Door: First of all, the pain the door causes would be significantly worse. But Insight Touch would allow the Sleeper to see that the door is, in some way, connected to the other two doors found in the other Sinkholes. One could determine that in some way, they are all the same door, yet lead to different places and are all presently locked. One could feel that death is heavily associated with the door (granted one could probably figure that out before touching it- but you know).

Sleeper Copies: Yes, their eyes may move and react, but their reaction is minimal. Destroying their own replica would not do much as they really are just unsettling replicas meant to (poorly) imitate the real Sleepers.