The player is free to decide in what order he/she wishes to activate any unit special abilities.

However, in this example, the faun does not lock the region. If the required conditions a met, the region will be automatically locked during step 2 of the domination phase. Otherwise, everything else is fine in both a) and b).

Page 13:

"Special abilities may only be activated when the player dominates a region”

No, you are not required to do so. You are allowed to use or not use abilities, in any manner you desire.

Locking of the region is not a Faun's ability. It is triggered by specific conditions. If they are met, the region has to be locked. So if Callo dominates a region with two nightmare tokens and Faun, it is locked automatically.

Yes, you can. Nothing changes, next turn Vuko goes to a different region anyway.

Callo may not replace the influence markers of other players if she has no influence markers of her own.

Page 14 

Acquired M-factor tokens have to be placed immediately on the player's character sheet on the spot labeled "0".

The player who has a unit with the pillage special ability gets to choose.

1. Player A gets to choose one of the available resources first.

2. Player B gets one of the remaing resources.

3. Player C may not get any resources from the region since his/her influence is too low. You need more influence than the neutral player in order to collect a remamining resource. 

Of course, a player influence in a zone may be altered by such factors as: special units in the region and/or the presence of Vuko in the region along with any Vuko tokens possessed by the players.

And if there is a tie for domination between players, please refer to Tied Domination on Page 13:

Tied domination: If two or more players have equal influence in a region,
then they count the sum of their influence in all adjacent regions. Whoever has
the most, wins the tie. If there is still a tie, the player with a highest position
on the reputation track dominates in that region (if there is a stack, the player
marker on the bottom wins the tie).

Vuko may only disable an influence marker per each Vuko tokens of yours. If you have no influence markers in the region with Vuko, you lose nothing. Special units grant their full influence whether Vuko is present or not, which is 3 in this example.

The Thorn only indicates the region where magical reserves should go, in order for them to be consumed by Van Dyken when achieving his individual goal. It grants no bonuses.

It cannot be done. The same applies to moving the magical reserve by the Ratling Piper during the activation phase. If you move the magical reserve towards The Torn, you may not harvest the M-factor from it when you dominate the region (another player dominating the region will however be free to do so). If you look at the order on page 12, you will see that the indvidual goals of a player must be resolved before resources are collected. 

Page 12:

The domination of each region, as well as the following actions, are
resolved in this STRICT order:
1) Determine which player dominates the region and the positions
of the remaining players.
2) Only the player dominating the region may use the abilities of their special
units, as well as accomplish their individual goal at this time.
3) Collect the resources from the region – the dominating player chooses
one of the resources available in the region and takes the amount listed
on the region token. Then the next runner-up player in descending order chooses
one of the remaining resources, and so on. Note: All resources are limited
by their available supply.
4) If there is a magical reserve in the region, the dominating player
also receives ONE token of M-factor. Magical reserve tokens are
non-exhaustive and may never be removed from the board by any
player other than Van Dyken when he absorbs it by use of The Thorn.

The resolution of domination in the region goes as follows:

1) Determine which player dominates the region

2) He/she can use their special abilities (the ones that may only be activated in the domination phase) to fulfill their individual goals

3) Determine the domination order of the remaining players

4) Take the resources from the region

Only victory points can be acquired once Callo locks a region. Thematically, the dream has occupied the region, so the resources do not technically exist. However, the area is still classified as under her control.