1. When the game ends due to not being able to refill Area cards, does the Refill Phase still complete in its entirety?
The rules are a little hazy on this but I say "Yes".
2. Since the last "special action" is performed in player order, does this necessitate retrieving workers in that last Refill phase to re-assess player order (lowest sum to highest sum)?
Once again the rules a bit unclear but I say "No". You leave all workers in place and just take your extra action in the current player order.
3. I acquire a Patron card and either can't/choose not to slide it into an available slot. I then use the card for its icon towards an Advanced Action. A patron slot then opens up and I add the card (which is on the right side) to the available slot. Later on, I acquire another Patron card and decide to immediately activate it in the slot that my previously-slotted Patron card occupies. Does it return to the right side of the board, or does it move to the left side and become "usable" again for its Advanced Action icon?
It moves to the left side. From rulebook p.8 "Note: It may happen in the advanced game, that when freeing up an active patron slot, a patron from the right side (used) can enter this slot. If you replace such an active card with a newly bought one, then it still goes to the left side. In this special case, you may use this patron card twice for extra actions."