The hop happens because of the physics engine.
The same link for my Utility Pack that I posted in the other thread. Using that, you can make your slopes as semi-solid actors, and the player or any other actor can smoothly move along the semi-solid, as you might be able to see in the sample game.
The 1-2 pixels is most likely because your animations are not all the same size for your actor, and the base of their collision boxes don't match, specially of their on ground and falling animations.