If I use Sylveon's "Wink Wink" attack to have my opponent discard Ilima, can I use Victini's "Victory Star" Ability to force my opponent to re-flip their coins?
Yes, you can. If your opponent flips a coin as part of your Pokemon's attack, you can use "Victory Star" to force them to re-flip those coins; but keep in mind you will have to re-flip your coins for Ilima too.
Source: TPCi Rules Team (2018-11-15)
If I use Sylveon's "Wink Wink" attack and discard my opponent's Diantha, can I get 2 cards from my discard pile even it 1 of my {Y} Pokemon was not Knocked Out on my Opponent's last turn?
No, you still have to meet the requirements of the card's text. You can discard the Diantha, though.
Source: Forbidden Light FAQ (2018-04-20), TPCi Rules Team (2018-05-03)
If I've already played a Supporter this turn and use Sylveon's "Wink Wink" attack, can I still use the effect of a Supporter I discard from my opponent's hand?
Yes. You are not playing a second supporter, but using its effect via an attack.
Source: Forbidden Light FAQ (2018-04-20), TPCi Rules Team (2018-05-03)