Got 36 moves just now. I wonder what the absolute minimum could be. It all depends on where everything is placed and if the monsta shows up in a stairway or door you need to use.
Rescued all.
Moves: 30. (Wow!)
Searches: 8. (7 would be the bare minimum: finding the 3 friends then -- no spoiler! -- doing what you need to do to find Dot.)
Attacked: 0.
I doubt I'm going to get any better than that. It really helps to not have to deal with things like finding fairies or searching the attic openings.