Gammadoodler
Hero
Not sure why the horse torso would pry anything. A horse can lower its head all the way to the ground. The human torso should be able to bend as far as necessary.And you also have the horse torso prying the human portion off of the cliff. It's leverage and weight. The centaur trying to climb that way has a suicidal death wish.
Sure. They use specialized climbing shoes. At least if they want to climb something sheer like a wall or cliff.
And in the same way humanoids might pack special boots, a centaur could pack special climbing gear as well, and probably would.
Note that this is also an discussion based 100% in your assumptions, which this far has included size, hoof type, applicable strength and now range of motion, aspects of character creation upon which the rules are (mostly) silent.