In most cases, the flapper should be replaced. Flappers are readily available in the plumbing aisle of your local hardware or home improvement store. You can also call your local plumber to replace it for you.
Yes, simply press the reset button on the control panel for 4 seconds until you hear a beep. Then push the lever down on the fill valve to allow water back in the toilet.
The water should be as close to the water line as possible. More than 1/8 of an inch away from the water line is too much. Always press the reset button for one second on the control panel to assure you have a green light.