Thanks,
oosyrag!
I tried native sizes and I tried setting "Collision Mask=Bounding box" for the floor and boxes, unfortunately it didn't help.
As for the drag&drop, I used it just for this demo, in a real game I have a different control system.
I am trying to do something with events - constantly checking if the box stays in the same place for longer than 0.1s, then changing its elasticity to 0, or even set it as Immovable, but it doesn't work very well. I really hope there is an easier solution.