This post tells you everything you need to know about how big you should make your mash/lauter tun:
Second, yes, recirculating (vorlauf) is usually done a few quarts at a time until there are not a lot of grain particles coming out in your wort. Once you aren't getting particles, you can just run off the wort into your kettle.
As for your question about lautering, I believe you're actually asking about sparging. Sparging is when you add new water to "rinse" the grain of all available sugar - lautering is actually the entire process of draining wort (which includes recirculating/vorlauf, runoff, and sparging).
As for how much you should be sparging with, I'm still new to all grain brewing so I use calculators. There are a number of great tools online that will calculate how much volume of water to mash with and how much volume to sparge with. There are lots of newbie-friendly recipes out there that will do the same thing, but remember that YMMV depending on your equipment.
Good luck and have fun!