The only stupid questions are the ones you don't ask! Also, any questions dealing with Sasquatches and cosmic eggs. Those are stupid as well.
It's not clear in the rules, so I will make sure to clarify that in the next FAQ.
It should be Critical Effects and then Unconsciousness Challenges, as that makes the most sense from a narrative viewpoint (i.e., "you suffer damage, and this is how it plays out. Do you manage to stay conscious?").
The character is probably unconscious for awhile, then. If they're Living, they've got natural healing that will eventually pull them above the threshold and let them regain consciousness. If they're a Construct or Undead, then the other Fated might have to look into some independent Artefacting or Stitching to get their companions up and moving again.