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


Why the bike should be "with the wheels level as the bike would appear on flat ground"?  
Why in position C I should replace gauge?  
Should I re-bend it with the same tool? How actually I re-bend the hanger?
Answering your questions about the Derailleur Alignment Gauge 


The bike is positioned level as it easier is to reference and reset the horizontal and vertical alignments.
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.
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.