I leave air in my tanks. They're designed to hold air and holding air won't damage them.
I unplug my air-rig and de-pressurize everything. I suppose you could leave everything pressurized, but why would you want to?
I remove my air-rig from my tank, but this is mostly because it's easier to pack everything down when the air-rig is off the tank.
I don't teflon tape anything that is meant to be screwed in and unscrewed on a regular basis.