Wesley,
Regarding footwork, both ways are taught but the jab step has become the more common method. The foot replace, in the opinion of many, is too much unnecessary lateral movement. That said, there is also the alternate method that should be learned with outside pitches where the right foot stays in place (no shuffle/jab) and the momentum and direction of the pitch allows the catcher to just continue turning and stepping into the throw.
Regarding blocking, you don't want to jump up at all but most often, you can't just fall forward/down either - rarely is the pitch perfectly straight in front of you. You want to square the ball up so the block is both a drop and an athletic lateral movement.
To illustrate both, check out the "catching 101" videos on youtube by Barksdale who is also a contributor here. The visuals in his videos are very good. At the end of the blocking drill video, there is a hockey drill. This drill will help you get quicker and stop from jumping up.