You can change the controls under options, controls. Then click a box and push an input. Though for me the arrow keys are already auto as a second choice for movement controls.
The best way to "deal" with enemies from behind is to time your jump. The special move also takes them out as well, but you only get 3 shots.
Yes, the slide has a cool down. The green bar at the top right is your indicator for when the cool down is done.