If Klefki with the "Wonder Lock" Ability is attached to a Pokemon as a Tool card, what happens if "Silent Lab" stadium comes into play? Does "Wonder Lock" shut off and Klefki get discarded, or does it remain attached to the Pokemon?
Once Klefki is attached as a Pokemon Tool card it retains its effect even when its Ability has been disabled. Once it's attached, it is essentially treated as a Tool with that text, so shutting off its Ability doesn't matter at that point. However, if something such as Lysandre Labs is in effect, Klefki won't be discarded at the end of your opponent's turn.
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.
If my opponent used Gardevoir EX's "Shining Wind" attack to gain "no Weakness" and I play Pokemon Ranger when it is my turn, does their Gardevoir EX have a Weakness again?
Yes. The ruling about effects on Weakness and Resistance not being ignored has to do with damage calculations [see "General Gameplay -> Weakness and Resistance" section for reference], not about whether a Pokemon HAS Weakness or Resistance. Pokemon Ranger removes attack effects, including this one; so yes, Gardevoir EX would have Weakness again after using Pokemon Ranger.