1. The Procedure section in Rule 3.2.2. says "flip all auxilia to revealed". Does that include auxilia that are not marching?I think you meant to write "flip all revealed auxilia to hidden", right?
If so then yes, all auxilia in the origin space are flipped to hidden. The same goes for warbands when other factions march.
You can even select (and pay for) an origin space without moving any units from there to other regions simply to flip all pieces there to hidden. The rules refer to this as "marching in place" on occasion.
2. The Exception to Step 6 of Rule 3.2.4. says "the Defender may opt to have any retreating Leader and/or Hidden Warbands stay put." Do those "staying-put" units take losses if the other retreating units are insufficient to absorb all the losses? The units that stay put are in no way different from other retreating units when it comes to assigning losses. If you wanted to you could assign losses to units remaining in the region before removing units that retreat to a different region.