I think I've confused myself on when a spell can be cast or displayed during an encounter-
Can the promo spell Embiggen (Freely display next to a local character) be played after an encounter has started? For example; Kyra encounters, displays Embiggen, then can attack or cast a spell (because Embiggen says freely).
In contrast Mirror Image just says Display. If Ezren encounters, displays Mirror Image; that's the spell for the encounter. In order to use an Attack spell, he would have needed to play Mirror Image before the encounter?
You can play Embiggen either before you explore, or whenever it would be relevant to a check. So, you can't display it if you encounter a monster with a "Before acting, take 1d4 combat damage" for the purpose of getting it out of your hand so it doesn't get discarded. But if the monster was "Before acting, succeed at a Dex 12 check or take 1d4 combat damage," you can definitely play it at that time to boost the Dex roll.
And yes, because it is "freely" played, that means Kyra could cast both Embiggen and Holy Light on the same combat check.
Mirror Image could also be played either before you explore or during an encounter when you take damage. The difference is that, because it's not 'freely', if you used a combat spell on the Check to Defeat and you didn't already have Mirror Image displayed, you could not play Mirror Image to reduce the damage if you fail.
Note this new rule which was NOT true in pre-Core:
" • Display: ... Displaying a card and immediately activating a power on it counts as playing it once, not twice."
So yeah, displaying and using Embiggen mid-encounter counts as single spell-play, and since it's "freely" - you're allowed to do it (subject to the usual "relevance" clause, as noted by MorkXII)
Note this new rule which was NOT true in pre-Core
I had something similar typed up, but Embiggen doesn't actually get 'played' once it's displayed.
Freely display next to a local character. While displayed:
.Exchange all of that character's dice for dice of these sizes: [dice list]
.At the end of the turn, banish.
So, even pre-Core, you could play it during an encounter for its effect.
Does this not count as activating a power on the card?
It doesn't count as "playing" it, which is the important part - exactly as per Mork's argument above about Embiggen. The clue you should be looking for is the word "may" (as in "you may...") - which signifies that you must chose to play the power. "Mirror Image" does NOT have it - so it's always in effect when applicable and you MUST apply the effect, even if for some reason you would prefer to take damage.