Best advice is to probably just leave it alone.
However, if you really want to get your volume back and have the materials on hand, you could potentially make a mini batch of the beer (thats enough volume to want to hop it) and dump it in.
How long has it been since the initial yeast pitch? I'm not sure you'd want to pitch that much wort on a beer that's ...
Let me answer your questions
You will need that 2 gallons of head space for foaming. Don't use a six gallon bucket.
Air is less of a concern during primary because of the volumes of CO2 produced but once the active fermentation has stopped, you need to be sealed in a carboy that is topped just a couple of inches from the bung.
You want as little headspace ...