Your controls on the air conditioner may have not been turned on properly to "air condition" and may have been set to just exchange air. You should hear the compressor cut in when you first start the unit up.
These units can freeze up. They can also be low on Freon. However you did mention that it had cooled well previously so it should be OK.
Leave the drain valves on the grey water and black water tank closed. When the black water tank is getting full drain it first and then the grey water tank. The grey water tank will "flush" the drain valves. You need to make sure your drain hose is sloped towards the park dump. Each time you dump the tanks you may want to add a chemical treatment to prevent odors. Do a search on the forum for holding tank chemicals -there will be lots of options. The tank monitors in your control panel may not be all that accurate. If you happen to get grey water come up in the shower pan - your grey water tank is full!! You can check the black water tank level by looking down into the tank thru the toilet when the flush valve is open.
You may want to get the propane tanks filled up so that you are not running out at some inopportune time. The filler will check numbers stamped in your tank and if the date is expired you will have to get the valves re-worked. The hose fitting threads are reversed from normal if you go to disconnect them.
The hot water tank should have lighting instructions stamped inside the door access when you open it.
Your stove should have a pilot light that you should light. Do a search on the forum to see how to do that.
Do you know if the power converter / battery charger has been replaced. The original ones tend to boil your battery over. The new "intelligent" converters do not do that. Again do a search on the forums and you can learn about that situation.
Place your fridge on electricity. Put a cheap thermometer inside to monitor the temp. There will be a control to set the temperature.
Do not go away from your site and leave your awning extended. Wind and rain can damage the awning. If it is extended drop one corner down a foot so if you get a sudden downpour the awning will not pool water. Search on the forum to see how to extend and retract the awning.
You may want to purchase an operators manual or the shop service manual for your coach. Sometimes they come up on the classified on the forums and also on e-bay. I think you can also get them from Airstream. I notice there are people putting them on CD's and selling them.
Do enjoy your A/S.
You can also ask questions on the forums