You'd need a much larger panel or multiple panels. Our kits are designed for lighting. The battery in your lawnmower has a large capacity so with solar panels you'd only be adding a top-up, it would help but unlikely to have enough output to be used all the time.
As long is the panel isn't sat in water the panel will be fine. Ideally, raise the panel just of the flat roof with a small angle to stop water sitting on the top.
Yes, the panel has pre-drilled holes on the rear.