#1
I play a lot of metal, system of a down, and rammstein, mostly, but power chords are a big part of metal. ive heard of two different types of chord: two finger, and three finger.
i have examples below of MY idea on this subject, and was wondering if anybody could correct me if i am wrong. (drop C, by the way)

three: two
d-------- d----------
a-------- a----------
f-------- f----------
c---4--- c---------
g-- 4--- g----4----
c---4--- c----4-----

by the way, dont remember which chord the one on the left is.
#2
I think two finger / three finger means how many fingers you use in the chord.
For drop tunings you might only need one, but in standard you have the

D| 10
A| 10
E| 8

shape. So you can either use two fingers ie, point finger on E string and your ring finger on the D and A string. Or, the three finger method, Point on E, Ring on A and pinky on D.
I use the two finger myself.
Some people use middle finger too but that seems weird to me.
Metal Head

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Squier Stratocaster
Jackson Pro Series Kelly
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Peavey Triple XXX Stack
#4
The 1st one is a power chord, the 2nd one is a "2 note power chord" that people play. I guess it is really up to you what to play, but I personally think you may as well play the full circle.

You generally play power chords using a barre in drop tunings anyway, so its not longer 2 finger or 3 finger method