Pressing space seems to equate to slamming the table upwards, but I want to do left/right movement. Is there any way to do this?

I've also read that there are two other buttons for slamming the table (one to the left of the right flipper button and the other to the right of the left flipper button), but they seem to do the exact same thing as space.

Z and /, according to the included instructions. and it doesn't seem to make much difference indeed.

Hitting the table while the ball is just rolling along doesn't do much of anything, Hitting the table from the right, with the </> key, will give you a lot more pop off of a band or bumper that is pushing the ball to the left, and will deaden things that are pushing it to the right. Vice versa for hits from the left with the <z> key. It has to be properly timed, just like on a real machine, but it does work.