Unbending Derailleur hanger

Question

Reading this article at park tool, it looks to be lacking some information, and here are my questions (some of them maybe pretty silly):

1. Why the bike should be "with the wheels level as the bike would appear on flat ground"?
2. Why in position C I should replace gauge?
3. Should I re-bend it with the same tool? How actually I re-bend the hanger?

Answer 1

Answering your questions about the Derailleur Alignment Gauge

1. The bike is positioned level as it easier is to reference and reset the horizontal and vertical alignments.
2. The wording around Condition C is a little vague. If the hanger is bent (as in Condition C), as you straighten it your original reference position will have shifted, so head back to 9:00 position to reset the gauge, then go back to position 3:00, and check the alignment again. If more horizontal straightening is required you will need to go back to position 9:00 and reset reset gauge after each straightening session, then head back to position 3:00 to check how you are doing on alignment. Repeat until straight or beer calls you away.
3. You will use the tool itself to bend the hanger back into position. You will want to put force on either the horizontal axis or vertical axis depending on how the hanger is misaligned. Keeping the bike level (Q1) makes this easier to do. Typically, I use the frame for leverage.

Answer 2

To align the derailleur hanger you don't need any special tools. At least with steel frames, the derailleur hangers can usually be bent without damaging them. Basically you have to do two things:

1. Check the derailleur hanger alignment
2. Bend the thing carefully until it is parallel with the wheel

For (1) you can use a spare rear wheel with a threaded axle. The axle threads are the same as the threads in the derailleur eye. Remove the derailleur and screw in the wheel instead. Use a spanner to tighten it a bit, so that the cone sits square against the derailleur hanger. With the now two wheels in place, you can measure the distance between the rims in several places. If the derailleur eye is straight, you should get (approximately) the same distance everywhere. If not, it will vary and you should be able to see in which direction the hanger needs to be bent.

For step (2), bending the hanger, you can use a large adjustable spanner. Align the spanner in the direction you want to bend the hanger and tighten it so that it holds the hanger well. Then bend carefully, preferably in the section between eye and dropout (and not at the "U-turn" of the dropout). I usually leave the back wheel in the dropouts and tighten the quick release, in order to give the dropout some support.

Bend a little, then check the alignment again and repeat if necessary. When done, carefully check dropout and hanger for any cracks! As said, steel usually survives quite a lot, but you don't want to risk losing your wheel because of a dropout failure.