Blur the Arc of Years (Fractured Days Split the Sky)

When instructed to "Repeat this Power", do you have to obey the range/target land restrictions?
Only if it doesn't tell you where to Repeat it. If a Repeat specifies where to use it, you obey those instructions instead of the usual Range and Target restrictions (p. 19) even if the land would normally be untargetable. In the rare case that the origin land matters when instructed to Repeat a Power in a specific land, it's the same origin land as the original power use.
For example, The Land Thrashes in Furious Pain could be Repeated on an adjacent land without Blight.
(Discussion elsewhere) Tags: Repeat, Targeting, Range, The Land Thrashes in Furious Pain, 19 more...

If an effect says that you may X to Y (e.g., paying Energy to gain a Power Card, Destroying Presence to skip an Event on a board), are you allowed to get the second half for free if you can't do the first half?
No, the second half is gated behind paying the cost in the first half. Similarly, "you may Y by X" requires paying the cost in the second half to get the effect in the first half.
While this tends to be pretty obvious when the cost is paying Energy, it's less clear if the cost is performing some other effect, like discarding a card or removing Presence.
While you must be able to pay the cost in order to get the bonus, ongoing effects can alter the final result of the cost being paid. For example, you can successfully pay the cost of "Destroy 2 Presence" even if "Flowing and Silent Forms Dart By" will end up saving that Presence from destruction if you do so. On the other hand, you can't attempt to pay the cost with Presence under "Absolute Stasis," since that Presence only exists for Victory/Defeat – it doesn't exist as far as the Event is concerned.
Tags: Action Modifiers, Absolute Stasis (Fractured Days Split the Sky), Turmoil's Touch (Wandering Voice Keens Delirium), Water Nourishes Life's Growth (Downpour Drenches the World), 11 more...

If an effect *(e.g., A Year of Perfect Stillness)* skips "all actions", what is affected?
Any time the Invaders would Ravage, Build or Explore that turn, any number of times.
This includes any normal actions that come from the Invader cards, and also any extra actions that come from effects like the power Manifest Incarnation or the event New Cash Crops Take Hold. (See the B&C rulebook, p. 15, for the distinction between "normal" and "extra" actions.)
(Discussion elsewhere) Tags: Skipping Actions, A Year of Perfect Stillness (Vital Strength of the Earth), Paralyzing Fright, Indomitable Claim, 4 more...

Can Invader Actions happen in a place that isn't a land (e.g., in The Endless Dark)?
No. If a Power would cause an Invader Action there (e.g., Manifest Incarnation causing a Ravage), skip that instruction because it can't be resolved.
Tags: Ravage, Build, Blur the Arc of Years (Fractured Days Split the Sky), Manifest Incarnation, 4 more...