Elemental Boon

If the Mentor Aspect gives another Spirit Elemental Boon, which Element Markers can they pick from? How about if it gives Gift of Nature’s Connection?
While not in play, Elemental Boon counts has having whichever Elements on it are most convenient, so Mentor can get 2 Element Markers of their choice when gifting that Minor Power. Gift of Nature's Connection, on the other hand, has no Elements printed on it, so Mentor gets only 1 Element Marker when gifting it.
Tags: Element markers, Elemental Boon, Gift of Nature's Connection, Mentor Aspect (Shifting Memory of Ages), 0 more...

If you gain a flexible Element (e.g., an "Any" Element, or multiple Elements separated by slashes) from something other than a Presence Track, when do you choose which Element to gain?
When directly gaining flexible Elements from an Action mid-turn, like from "Absorb Essence" or Lure of the Deep Wilderness’ 3rd Growth option, you must choose a specific Element immediately.
Passive Elements on Presence Tracks or in Bonus Spaces can be chosen at any time. [Core rulebook, p. 14, last item under Presence Tracks]
Tags: "Any" element, Elements, Growth, Presence track, 9 more...
Are elements personal, or can you use elements from other spirits?
Elements can only be used by the spirit that played them; they can't be shared unless an effect explicitly says so.
For example, if you are playing River Surges in Sunlight, you cannot use water generated by cards played by Ocean's Hungry Grasp.
There are a few power cards that grant elements to other spirits, like "Elemental Boon," the innate power "Spirits May Yet Dream" from Bringer of Dreams and Nightmares, or several of Serpent Slumbering Beneath the Island's powers. Powers with this effect are specifically marked.
Tags: Elements, Elemental Boon, Gift of Nature's Connection, Spirits May Yet Dream (Bringer of Dreams and Nightmares), 8 more...

Which elements does Elemental Boon have for the purpose of Events?
It is your choice (Branch & Claw rulebook, p. 16).
This is true whether you are discarding the power as a randomizer, or discarding/forgetting it to get +2/+4 Energy for Choice Events.
(Discussion elsewhere) Tags: Discarding Powers as a randomizer, Choice Events, Elemental Boon

If Gift of Nature's Connection comes up as an Event randomizer, does it work like Elemental Boon (we get to choose if it has the element or not)?
No, treat it as it appears - it has no elements. (Unlike Elemental Boons, which has question-marks.)
In hindsight, this is how Elemental Boon should have worked, since it avoids an exception case / specific rule just for it.
Tags: Choice Events, Gift of Nature's Connection, Elemental Boon
In a solo game, do you get bonuses on powers like Boon of Vigor that usually only happen if you target another player?
No.
You can target yourself with powers that say 'Another Player', but any effects that are conditional on targeting someone else do not activate. (Rulebook p. 22)
(Discussion elsewhere) Tags: Solo games, Boon of Vigor (River Surges in Sunlight), Gift of Constancy, Elemental Boon, 6 more...
If you Repeat a Power card with "Powerstorm" or "Gift of Strength," do you get double the elements?
No, you only get the elements once, when you play the card (p. 19, under Repeat).
If you Repeat a Power card that explicitly grants elements (like "Elemental Boon") then you do get the benefit twice.
(Discussion elsewhere) Tags: Repeat, Elements, Powerstorm, Gift of Strength (Vital Strength of the Earth), 7 more...