The walljump is a little finnicky, yeah - you need to hold the button against the wall, the tap jump.
Also I'm not sure for your other question - the way the game works is the button timer goes down as long as the key is held, and each timer maxes out at 1 second. Theoretically tapping it would work, it'd just drain for as long as you tapped.
Hope it was ok for you, regardless!