How do I do it without pressing F?

Hold down Z while you move the mouse.

This also works with the X and Y axis. (whole holding down X or Y)

And how do I turn off the rotation tool?

You can't.

You rotate objects by moving the Mouse laterally, while holding down the Right Mouse button. (holding down X, Y, or Z will rotate along that axis)
But you move objects with the Left Mouse button, so there's no need to disable rotation.
You can toggle Snap to Angle on/off if you like, but you still rotate objects the same way. (the red angle button, top right in the CS... perhaps that's what you mean?)

Perhaps you should check out a CS tutorial. http://www.tamriel-rebuilt.org/?p=modding_data/tuts/dsong/first_room is good for beginners.

Oh wow. I've just been going off Silvermagic's Shack Tutorial.