Thank you for playing!
In Level 2 and onward, you always need to select a Charger (the yellow things in the bottom) for the run button to be enabled, even if you could potentially reach the bulb already.
Yes, the battery level "registers" on a click, i.e. if you move the mouse slightly, the number on the UI element is different than the actual amount of steps / time.
Sorry for the inconveniences!