Trainers » Lysandre Labs | Trainers » Silent Lab | Abilities » Wonder Lock
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.
Source: TPCi Rules Team (2019-01-03)
Trainers » Silent Lab
If Silent Lab stadium is in play and one of my Basic Pokemon evolves into a BREAK Pokemon, would it be able to use the Ability from the underlying Basic Pokemon or not?
When it evolves into a BREAK Pokemon it is no longer a Basic Pokemon, so Silent Lab no longer affects it and you would be able to use the underlying Basic Pokemon's Abilities.
Source: TPCi Rules Team (2016-06-23)
Trainers » Silent Lab
Does "Silent Lab" stadium shut off "Alpha" and "Omega" abilities?
No, those are considered Ancient Traits, they are not Abilities.
Source: Primal Clash FAQ (2015-02-05), TPCi Rules Team (2015-02-05)