To push on the leading edge is not recommended as it is soft skin and can be bent. Any a/c can be pushed by the prop as long as it is done near the hub. NEVER push by the prop tips as they might bent! Cessna can also be pushed by the struts. Also, not recommended to push by the wing tips (Force X Arm = Moment).
Regarding the other question, ‘Why not to push down on the end of the a/c’. I remember reading many years ago that Cessna published a warning not to do so as it creates high stress on the tail assembly which in turn cause cracks, especially if done by pushing the stabiliser. If the a/c is fitted with handles they can be used to lift the tail while turning the a/c.
It is bad practice to push on the tail cone but many are doing so including mechanics, I told mine off.