I can't give you a full solution, but I can offer some improvements. (I'm pretty much a physics newbie too)
The resting on the floor problem can be improved greatly by using the native size of your floor object, rather than stretching it at runtime, due to rounding errors.
The janky movement when dragging is caused by using a non physics method of moving around the object. As mentioned on the manual page, this is normally not recommended (drag and drop can't take into account collisions and center of gravity rotations ect, so the two behaviors will fight each other to position the object).
I'm not sure whats going on with the two boxes resting on each other. Again try to make sure that the native size of the object matches what is placed in the layout editor to minimize rounding errors, although this didn't seem to help in this particular example.