Days that Never Were (Fractured Days Split the Sky)

Do effects that interact with “gaining” Power Cards apply to every time a Spirit gets a new Power Card, no matter the method?
No, only if the Spirit explicitly “gains” that Power Card (usually by drawing four cards and picking one to keep). If they “take” a Power Card, are given a Power Card, or otherwise receive a Power Card without being told to “gain” it, then they have not “gained” a Power Card.
Tags: Gaining Power Cards, Taking Power Cards, Transferring Power Cards, Gather Power from the Cool and Dark (Shroud of Silent Mist), 14 more...

If you gain a Major Power by non-standard means or from a place other than the Major Power deck, do you have to Forget a card? How about the "gifting" of Entwined Power's threshold or "taking" a Major Power?
"Gifting" is a transfer and does not require Forgetting, and "taking" explicitly doesn't require Forgetting. But for any Gain of a Major Power, you must Forget unless the effect specifically exempts you.
As usual, you may Forget the Major Power you just gained, if you'd prefer that to losing any of your other Power Cards.
(Discussion elsewhere) Tags: Gaining Power Cards, Forgetting, Taking Power Cards, Transferring Power Cards, 7 more...

Does Destiny Unfolds have any effect on taking powers (e.g., via "Transformative Sacrifice") or gaining powers from a specific subset rather than from the deck (e.g., "Let's See What Happens")?
No, those effects work normally, since they either aren't “gaining,” or are gaining from a place that is not specifically a power deck.
Tags: Gaining Power Cards, Taking Power Cards, Aid from Lesser Spirits, Let's See What Happens (Grinning Trickster Stirs Up Trouble), 10 more...
When Fractured Days Splits the Sky plays Destiny Unfolds and gains a card from their Destiny, do they also put a card in Days that Never Were?
Yes, and they can usually put any card they could have picked from their Destiny into Days that Never Were; they don't have to pick a Power Card of the same type as the one they gained unless the gain effect had a restriction.
Tags: Gaining Power Cards, Days that Never Were (Fractured Days Split the Sky), Fractured Days Split the Sky, Destiny Unfolds, 0 more...