Spur on with Words of Fire

If you gain presence during the turn (after Growth) and uncover the "any" or another element, can you then use it for other powers?
Yes, you can start using elements as soon as you gain them. (p. 14) Similarly, if you are able to play a card mid-turn, you get the effects of its Elements immediately.
(And if some effect were to cover an Element by returning Presence to your track, or destroy a Power card in play, you'd immediately lose access to the elements.)
(Discussion elsewhere) Tags: "Any" element, Elements, Adding Presence, Indomitable Claim, 13 more...

When an effect lets you play a card, does that count against your allowed number of card plays?
No. The number of card plays on your Presence track only affects how many cards you can play as part of the "Play and Pay For Power Cards" action in the Spirit Phase. Cards played any other way (usually in the Fast Phase when instructed to do so by a Power) are in addition to those limits.
(Discussion elsewhere) Tags: Playing Power Cards, Spur on with Words of Fire, Unlock the Gates of Deepest Power, Gift of the Primordial Deeps (Serpent Slumbering Beneath the Island), 14 more...

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...

When playing Ward the Shores, if you play a Power Card not during the Spirit Phase, can you play it face-down to add a warding pattern?
Yes, subject to the "once per turn" limit.
(Discussion elsewhere) Tags: Playing Power Cards, Ward the Shores, Spur on with Words of Fire, Gift of the Primordial Deeps (Serpent Slumbering Beneath the Island), 4 more...