If you understood "gyroscopes", then you wouldn't ask question 1. That's what's happening - think harder about my question about lift. I'm not going to repeat myself for the third or fourth time.
If you think the gentle reaction force on a skid tip matches the lift force that raises a helicopter off the ground, and acts further from the center of mass, then you need to reconsider. What lowers the skids to the ground? Reducing lift and allowing the aircraft to settle. The skids don't provide a couple to the rotating part, but to the stationary part. That has no effect on the rotating parts.
You seem to be obsessed with a spinning top toy that has a huge angular momentum to mass ratio and no couples acting apart from an azimuthal drag and a gravitational turning force. That's why I again suggest that you drop this toy "gyroscope" fixation and consider instead the physical reality of the rotating objects.
This guy's description is broadly correct:
Pitch Control
You can argue yourself blue, with a theology that rotors don't behave like any other rotating object, but physical reality is still going to be what it is.