Tuning is a three part process. Tune the archer, tune the bow and tune the arrow. Each part has to be working together for the best accuracy and best arrow flight.
I notice that you live in Maryland. You might consider taking advantage of this seminar:
http://www.huntingnet.com/forum/tm.aspx?m=2092861
You can also download the Easton Tuning Guide from their website, but it is a little confusing since it discusses tuning for all types of bowsat the same time. It is also beginning to get a little dated.
To answer a couple of your questions:
If you are bow hunting, you want the best arrow flight as well as accuracy so for the basicsyou tune the arrow to the bow and to the archer. However, there is a lot more to it than this.
For outdoor target shooting, you also tune the trilogy because you are shooting are different distances.
For indoor tournement shooting at one distance, you only need the arrows to match as perfectly as possible. You don't really care how they fly as long as they fly to the X every time. Again, there is a lot more to it than this.
Aluminum vs. carbon arrows - carbon arrows are less critical of spine matching than are aluminum arrows. The basic tuning techniques are the same. Arrow spine selection is a little more important with aluminum arrows.
Adjusting or twistingnocks is one of the last things that you do during tuning. Once you have the trilogy tuned for one arrow, you are shooting to determine which arrows shoot together. Every dozen of arrows have some that for some reason, won't group with the others. Generally, the more you pay for your arrows the better the yield. However, this is not always the case. Nock alignment is one of the biggest reasons that one arrow doesn't group with the others. Twisting the nock will sometimes align the nock. Sometimes not.
As I've mentioned, there is a lot more to it than this.
Check out Len's seminar. He addresses all of these problems several times every day.