Welcome to the forum! Märzen isn’t my favorite style so good choice.
1) as long as the beer has finished fermentation you can go ahead and cold crash it without having to worry about dropping temps a few degrees per day.
2) you’ll want to place something in the neck of the carboy. Cold crashing creates a vacuum so if you use an airlock air and/or your fluid will get sucked back into your carboy. After racking to your secondary use several layers of plastic wrap fixed with a rubber band. Don’t make it tight as the vacuum could tear it.
3) the longer you lager it the better. In time the trub and yeast will settle out as well as any Polyphenols and tannins.
You didn’t mention how you’ll be packaging the beer so I’m assuming you’ll be bottling. If bottling you could go ahead and bottle condition now and once carbonated place the bottles in the fridge. This would eliminate any concerns of oxidation created by a vacuum. If your kegging, use the keg as a ‘secondary’ and lager in the keg.