Hi Punch,
I've been using compressors for 20 years. I myself tend to always leave some amount of air in the tank, if anything, just for the convenience of being able to just walk up to it and grab the hose to add air to my car tires. I hate having to wait for the tank to charge up..LOL I don't see that it would hurt it at all, but if it won't be used for a long time, I certainly would reach underneath the tank and drain the water from the tank from the release valve. In case you don't know, there should be some air in the tank so the air pressure being released will also help shoot as much water out as possible.
As for your second question, having a good supply of air as close as possible to the pneumatic prop ensures that adequate pressure is available for the best triggered effect, especially if the compressor is far away from the props causing you to have a very long pneumatic hose run. I very much doubt the compressor will be running all that much to maintain proper charge to the second storage tank. Unless you're going to have loads of kids constantly walking by, I wouldn't worry about it. Take lots of photos for us :::smiles:::