Do we need to say "down"? It's not going to fall up.
No - down is NOT needed
And then Newton had this great idea...
I guess you are saving "az alma nem esik messze a fájától" for a future lesson.
Why not falls off the tree?
Perhaps there is a different Hungarian pre or postposition for "off" specifically
No - my dictionary gives "falls down" or "falls off" for leeszik