Make any settings in the projector you want/need and then calibrate it if it you (if you make the settings too extreme you probably won't be able to calibrate it). Then, don't change the settings :-)
Using extended display...good question. When you profile it (which should be done in a completely dark room, yes), your tool should identify both screens individually and let you calibrate them. Unless you have a very old operating system, it shouldn't be a problem loading both profiles but you may want to ensure the projector is on before you boot so it's detected at startup.