If the underside of the shed is accessible, ~ 2mm thick plastic washers fixed with galvanised clout nails at 30cm or so spacing can be effective to create an air gap, so that even if the timber gets wet it can then dry out.
If both floats are under water (as it seems in the pics), then the float valves are faulty and water will overflow somewhere when your stop-cock is turned on.
Tie up the ball valve on the F&E tank in the loft temporarily, in case the valve is passing slightly and generating a vibration. Are there any drips from the overflow of that tank?
Sounds like a loose wire connection in the light fitting or switch. Isolate the lighting circuit, check it is isolated, get your screwdriver out and ensure all screws are tight in the fitting and switch..