If you carb 12 PSI at room temperature, you are going to get about 1.45 volumes CO2 - likely significantly undercarbed unless you are doing certain English styles. Disconnecting the gas and cooling the beer will not yield any higher volumes of CO2. You need to either carb at a higher pressure...
If you do it the way described above, the kegs will eventually equilibrate to whatever volumes of CO2 your "serving pressure" will maintain. Serving pressure should be set to maintain the desired volumes of CO2, so you would need different pressures to keep two beers at the same temperature but...
The 575's are creamer faucets that whip air into the beer when the faucet handle is pushed back to get a creamier head. I don't think you'd want that for seltzer. Maybe for soda, though. I would think standard 525's would work just fine for both applications.
Not sure about cheap...I have a couple twelver's of 16 oz flip tops from Schwelmer's hefeweizen and a case of Hacker-Pschorr flip tops from their Sternweisse. Try the import aisle...the flip tops are pretty easy to spot.
Keep in mind that pin lock kegs are larger in diameter than the more common ball lock kegs. If your source that said you could fit 6 in was based off of ball locks, you should double-check your figures before committing to pin locks (or 6 faucets).
Oxygen is not in the liquid state at the pressure inside a medical gas cylinder. CO2, however, is. Tipping a CO2 tank on its side is a bad idea unless you want to mess up your regulator and potentially cause a dangerous situation.