How does Infinite Reflection work with Commander and commander damage?
I found the answer to this in the rules:


  903.3. Each deck has a legendary creature card designated as its commander. This designation is not a characteristic of the object
  represented by the card; rather, it is an attribute of the card
  itself. The card retains this designation even when it changes zones.
  
  Example: A commander that's been turned face down (due to Ixidron's
  effect, for example) is still a commander. A commander that's copying
  another card (due to Cytoshape's effect, for example) is still a
  commander. A permanent that's copying a commander (such as a Body
  Double, for example, copying a commander in a player's graveyard) is
  not a commander.


So the answer is that in the first example (commander copying Malignus) the antagonist loses the game. In the second he/she does not (yet).