at least when you use the controller you can alter your movement speed by not fully push the stick forward...does a slower movement speed favor your sneak attempt? thats at least my perception but i could be wrong...?

Running, even while crouched, gets a penalty to your sneak check.

how can you toggle between running and walking? i only find an option for sprinting?

In Oblivion shift was the modifier. With capslock being a toggle.

and with a controller? is it simply measured by the amount you push the stick forward?

That is correct, sir.