All appliances will have a UL sticker which lists the voltage requirement and amperage draw of that appliance. Multiply the voltage times the amperage and you'll get the wattage required to run the appliance. As long as you don't exceed the 400W supplied by the truck's inverter you should be okay. Keep in mind that most appliances with electric motors require a heavy draw in the instant that they're started, so even if the wattage rating is below 400W for that appliance, the instantaneous startup may trip the inverter's fuse (assuming it has one).
I was thinking of getting a 1000W from Harbor Freight
for my truck. They're relatively cheap if you need something with a little more capacity.
Oh, and draining the battery depends on what you're powering with the inverter. Higher amperage will drain it much faster. The air compressor you want to use is, I assume, for an air mattress? If it's one of the cheapo ones that comes with the air mattress, then you''re not likely to drain the battery even with a few hours of continuous running. The electric fryer is a different story though. I doubt that the inverter will even handle that with the truck running.