Hi,
Simple Green or another dish soap will work fine on the A/C unit, however it is very slippery, so keep yourself on the ladder side of the soap, and spray the roof in that direction - away from the ladder, so it does not become slippery. Have a towel up on the roof, in case you need to kneel on it, or to walk across if some slippery soap gets in between you and the ladder.
Use a garden hose to wash off the A/C unit. This will improve air flow for the outside coil, and aid in getting rid of all that heat.
The square grill in your ceiling should be the 'return' air grill (and be larger than the others) and contain the air filter. Rinse it out in the sink or bathtub. Normally I just put it back right away, it can dry itself out while running the A/C unit. With the cover off, you can look for ice on the indoor coil. If it has been covered with ice, then run the fan all the time to get rid of any ice on it, in between cooling cycles.
Running on high fan speed, you are less likely to have ice build up on the coils.
Run your refrigerator on gas, and the heat input to the boiler (where the cooling starts) is double the capacity on electric. Also you will be using 3 less amps in the RV, and voltage to the A/C unit will be slightly higher. So on days over 90F, I would always change my refrigerator to gas. You can change back to electric at night, or just run it on gas and remember to fill the tank every 6 weeks or so.
While you have the garden hose and soap out, you might as well clean the radiator coils on the engine too! It will increase the cooling capacity of the dash air as well. Just spray on some soap, and rinse with the garden hose. If you have a "No cleaning vehicles" policy at your campground, do this discretely, and do not wash the outside of the vehicle, just the radiator that you can see. It will get a lot of bugs on it just driving around, and that reduces the cooling ability of your vehicle.
Good luck, and have fun camping!
Fred.