Research this site for your carb. They have listings with the various suffixes and note that most still use the same carb.
https://www.jackssmallengines.com/jacks-parts-lookup/manufacturer/kawasaki/4-stroke-engine/fd501d/fd501d-fs00-4-stroke-engine-fd501d/carburetor
A sheen on the water is not normal in any circumstances. I suspect it is running rich.
Since the spark plug replacement did not eliminate the sheen entirely check the choke operation. It is controlled by a bimetal spring heated electrically. They go bad after time and unfortunately the spring...
If the airplane is on a non-moving treadmill in a large wind tunnel providing a wind speed of 200 knots do the wheels need to turn for the airplane to take off?
The heat exchanger is will be empty when not running in most installations.
The 5e has 2 shutdown sensors.
1. Disconnect the exhaust over temp sensor and see if that has any effect.
2. Verify oil level, disconnect the oil pressure sensor and see if that has any effect.
3. Verify spark and...