Sacred Sites under Threat

When the Dark Fire Aspect discards a card with both Moon and Fire to pay for a choice event, how much Energy does that count towards the cost? How about if it forgets the power card isntead?
2 Energy and 4 Energy, respectively. The discard and forget options for Choice Events check if a card has a relevant Element, not how many of that Element is on the card.
Tags: Choice Events, Elements, Sacred Sites under Threat, New Species Spread, 2 more...

When does destroying a Town or City cause Fear?
Always, regardless of how it's destroyed: directly via a Power that says to destroy one, from damage done by a Power, from damage done by Dahan counterattacking, due to a Spirit's special rules, from a Fear or Event card, etc. [p. 18]
Fear from destruction is independent of any explicit Fear the Power does – e.g., Lightning's "Shatter Homesteads" reads "1 Fear. Destroy 1 Town." usually generates 2 Fear: 1 explicitly, and 1 for destroying a Town.
Note that when you remove or replace a Town or City, it does NOT cause any automatic Fear. Removing Invaders happens most frequently via Fear Cards, and usually represents the Invaders fleeing, which doesn't make them any more afraid. Replacing an Invader represents some sort of transformation or change; if it's a scary change, the effect will explicitly specify how much Fear to do.
(Discussion elsewhere) Tags: Destroy, Fear, Dahan, Ravage, 51 more...

On the Event card Sacred Sites Under Threat, what are the choices we are choosing from?
You are choosing between the two bold-faced headings: 'Let the Island's Strength Repulse them' and 'Guard them Yourself, for Well or Ill'. If you choose 'Guard them Yourself, for Well or Ill', then there is a further choice for each Sacred Site with Invaders.
On the further choice, in each relevant land (no matter how many Spirits it's a Sacred Site for) you basically pay 3 Energy to deal 2 damage; or else pay no Energy and destroy 1 Presence from each Spirit there. The total Energy cost for dealing Damage in one or more Sacred Sites is paid all at once by the Spirits collectively; Fire only reduces the total cost, not the cost per Sacred Site.
(Discussion elsewhere) Tags: Choice Events, Sacred Sites under Threat
Can Events on an Event Card be resolved in the order of your choice? (e.g., to get the benefit from "Canny Defense" during the Ravage cause by "New Cash Crops Take Hold" earlier on the card)
No, the Events on a card are executed in order from top to bottom, so the extra Ravage takes place before you get the benefit of "Canny Defense."
Likewise for "A Strange Madness Among the Beasts," the Beasts deal damage after the first part of the card (in which some of them may be removed).
Tags: Events, Ordering, New Cash Crops Take Hold, Canny Defense, 19 more...

Can the same piece be moved multiple times with the same Event or Fear card?
Yes, as long as any restrictions on the card are obeyed.
For instance, the same Explorer can move multiple times with the Fear card 'Retreat!', and the same Beast can be moved multiple time with 'A Strange Madness among the Beasts'.
If the card says players must make different choices, this must be obeyed.
(Discussion elsewhere) Tags: Events, Fear, Gather, Push, 11 more...

If an effect moves pieces "on each board," "in each land," or for "each Spirit," can the same piece be moved multiple times?
Yes, assuming that it separately meets the condition to be moved each time. For example, "Beasts Chase Off Homesteaders" ("On Each Board: Push up to 2 Explorers or 1 Town from a land with Beasts tokens.") can Push a Town multiple times, so long as the Town keeps arriving in a land with Beasts tokens that's on a board where "Beasts Chase Off Homesteaders" hasn't resolved yet.
Note however that while an "each [piece]" Event/Fear/Adversary effect does create one action per land with that piece, each piece of that type only participates in one of those actions. For example, while "Beasts Prowl" ("Each Beasts token generates 1 Fear if Invaders are present, and moves to an adjacent land if not.") can move a Beasts token into a land that already has Beasts tokens, the newly-arrived Beasts token doesn't participate in the "Beasts Prowl" action there – only count the Beasts that were already there before resolving "Beasts Prowl."
Tags: On Each Board, Actions, War Among the Dahan, Spreading Conflict Prompts Caution, 26 more...