The picture could be deceptive but that water sure looks inky black!
To rule out cylinder head issues invest in a compression tester. Draper do one for £25 so it won't break the bank. Remove both spark plugs and screw the compression valve into the spark plug thread. Turn the engine over and take a note of the reading. Both cylinders should be within a few PSI of each other.
If that's not conclusive, run the engine and lightly feel around the head gasket for any fuel/oil once it's been cleaned up prior to starting.
The carbs needs to be removed and completely stripped down. Use the right size screwdrivers to remove the jet nozzles and ensure air passages are clear with compressed air. Soak in carb cleaner, thoroughly wipe down with a clean cloth and reassemble. Don't adjust the fuel/air pilot screw. If you are going to check, then screw in (counting the number of turns) until lightly seated. I'd have thought it would be 1 1/2 turns out.
If the 'o' ring where the carb meets the engine head block looks worn, then go ahead and replace.