Arsene Renard (The Key and the Gate, F54) reads:
Response: After an opponent plays a support card, search the top 5 cards of his deck for a support card and put that card into play under your control. Then, place a success token on Arsene Renard. If that card is still in play at the end of the turn, sacrifice it."
Q1.i) If Arsene Renard triggers his ability to search the top 5 cards of his opponent's deck but fails to find a support card, does he still place a success token on himself?
No he does not. Everything before the "Then" statement must successfully resolve for the success token to be placed.
I'd also like to understand the general rule(s) being applied to decide this...
Q1.ii) The FAQ says in 2.3 'If Able' that: "If a “Then” effect follows the “if able” effect, all designated cards and players must have had the effect successfully resolve in order for the “Then” effect to resolve."
Is this FAQ entry intended to be a clarification for "if able" cards, to indicate that they are to be treated the same as other cards without "if able"; or does this requirement for successful resolution only apply to cards where "if able" is specified (unlike Arsene Renard)?
As I said above, the "Then" effect is conditional. Every part before the "Then" must resolve successfully for anything after to even be attempted.
"If able" means you will make an attempt to resolve every part of the effect on every designee, and not being able to resolve it on everything designated by the card does not prevent the entire effect from resolving on those designees that it can resolve for.
An effect which says "If able" for the first part of the effect and is followed by a "Then" effect will resolve on each designee and for those designees that had the "if able" effect successfully resolve will then resolve the "Then" effect, while those designees who could not successfully resolve the "If able" effect will not attempt to resolve the "Then" effect.
Here is the example, I play a card that says, "Action: Each player with 5 cards in hand draws 5 cards, if able. Then, discards 2 cards." If I have 5 cards in my hand and you have 2, I get to draw 5 cards. You draw nothing. Now because I drew 5 cards, I discard 2. You discard nothing.
Doesn't that contradict the example given in the FAQ under 2.3 "If Able", below, which states that unless everyone is able to fulfil the requirement then nobody proceeds to the "then" statement?
"For example, Darrin’s opponent Tommy has Feral Elder Thing (Revelations F78) in play with the text, "At the beginning of your turn, each player chooses and discards 2 cards from his hand, if able. Then, each player draws 1 card." When Tommy’s turn begins Darrin has 3 cards in hand and Tommy has 1. Darrin choose and discard 2 cards, but Tommy is unable to choose 2 cards to discard. Since both players were unable to discard 2 cards, neither player is able to draw a card."
(Or is the difference that you've added the "with 5 cards in hand" limiting condition?)
Correct, because 1 player did not meet the requirement to be designated they are excluded from the entirety of the effect. I was attempting to give you another explanation that differed enough from the one in the FAQ so that you could get a better idea of the general rule.
Q1.iii) The FAQ says in 1.10 'Eligible Targets' that "In order to target a card with an effect, that card must meet the targeting requirements. Any part of the effect for which that character is ineligible is simply ignored."
If a component is ignored (e.g. Arsene Renard's instruction to "put that card into play under your control" in the instance where no support card is found), is it also ignored when determining whether or not to trigger a subsequent 'then' effect; or by ignoring it does that automatically preclude from being able to trigger the following 'then' instruction?
This has nothing to do with Arsene. This is specifically for cards that direct you to target a card in order to play it. If the card does not say choose to designate there is no target.
Q1.iv) The FAQ says in 'Frequently Asked Questions' that:
"If a card requires something like “destroy all Day cards, then...” is it possible to satisfy this requirement if there were no Day cards in play at the time? In other words, can you destroy 0 cards?
Yes. The requirement is to destroy all, whatever number that is, including 0, as long as you have done that the “then” effect will trigger. If a card gave a set number, you would have to meet that number."
Does this logic apply to Arsene Renard, that searching, finding 0 and putting in to play 0 support cards has met the initial requirement to invoke the 'Then' statement to place a success token on himself? Or does such logic only apply in instances that effect "all" corresponding instances?
Again this has nothing to do with Arsene because his card effect does not use the word "all."