Interesting experience. I cannot answer to the air pressure thing, but I can offer a suggestion for the cleaning aspect. I too pour any remaining paint into the jar it came in. I also have two of the airbrush cleaning bottles that you can spray into to remove anything in the brush. One I use when I'm cleaning out the cup. They way I clean my cup is this: first I get a small spray bottle with an adjustable nozzle and set it to 'stream' and I fill it with Lacquer thinner. You can use any cleaning medium you wish. The small spray bottle I use can be gotten from one of those stripper kits for stripping shellac from wood surfaces. After clearing the interior of the airbrush by spraying it into one cleaning bottle; I then tip the airbrush cup over the mount of one of the cleaning bottles and spray the stream of thinner in the cup, letting it run out and into the cleaning bottle. I keep spraying until it runs clean. Then I add some more thinner/cleaning agent to the cup, cover the needle end with a paper towel and backflush the brush. I then pour out the remainder and spray the remaining interior cleaner into the other cleaning bottle. I repeat until the backflush comes clear. After that; if I still need to break it down to clean, I do.
Sorry I couldn't be more help with the rest of your questions. Hopefully soon, others will be here to offer more excellent advice.