I think it is highly unlikely that they use chakra to break their fall when they land, since it does not mention it anywhere. Take the tree-climbing exercise for example. Naruto goes up a few meters, then lands straight on his head. Did he use chakra to break his head-fall? Probably not. He lost focus of his chakra, and that was the cause for his fall. Would this fall have caused serious injury or death to a real person? Yes.

Granted, this moment was probably intended for comedy, so you can take a more serious note - Naruto climbs up pretty high (about how high sasuke was on his first try) and then falls down and lands on his feet. Is it likely that he could re-focus his chakra to his feet, mid-fall, right after it was lost to make him fall in the first place?


Now, for your other question...

A person or creature's leg strength is directly proportional to their cross-sectional area, like the columns that hold up greek temples. This, in turn, is proportional to the square of the radius of the column, according to the equation -
A= pi times r squared
So, the strength of legs scale up with the square of the scaling factor (hence, 100 squared)


Somewhat similarly, each segment of a creature's body is about the same as a sphere whose weight is proportional to its volume given by the equation:

V=(4/3) times pi times r cubed

With constant density, the weight therefore increases with the cube of the scaling factor.