I have 5 Pokemon on my Bench, and 2 of them have the "Omega Barrier" Ancient Trait. If my opponent plays Avery and I choose the 2 Pokemon that have "Omega Barrier", do they get discarded or is the effect of Avery blocked?
Yes, they get discarded. The discard effect of Avery is on you, the player choosing the Pokemon, not on the Pokemon with Omega Barrier.
Source: TPCi Rules Team (2022-01-20)
I have 3 Pokemon on my Bench, and 1 of them has the "Omega Barrier" Ancient Trait. My opponent plays Cyrus {*}, and I choose to keep the 2 Pokemon that don't have "Omega Barrier". Does the Pokemon with "Omega Barrier" get shuffled into my deck?
Yes, it does. The effect of Cyrus {*} is on the player, not on the Pokemon with Omega Barrier.
Source: TPCi Rules Team (2018-05-31)
If I play Captivating Poke Puff and find a Pokemon with the Omega Barrier Ancient Trait in my opponent's hand, can I choose that Pokemon to be benched or does Omega Barrier block the Captivating Poke Puff?
Yes, you can put that Pokemon onto the Bench. Ancient Traits are only active when that Pokemon is in play.
Source: TPCi Rules Team (2017-03-30)
Can I play Target Whistle and choose a Basic Pokemon in the Discard Pile with the Omega Barrier Ancient Trait, or does Omega Barrier block the Target Whistle?
Yes, you can put that Pokemon from the Discard Pile onto the Bench. Ancient Traits are only active when that Pokemon is in play.
Source: TPCi Rules Team (2017-03-30)
If my opponent's Active Pokemon has the "Omega Barrier" Ancient Trait, can I use Lysandre to switch one of my benched Pokemon with it?
If your opponent's Benched Pokemon has "Omega Barrier", then Lysandre's effect will be blocked. But choosing a Benched Pokemon without "Omega Barrier" will cause it to switch with the Active Pokemon because the Benched Pokemon is the target of Lysandre.
Source: TPCi Rules Team (2015-04-09)
If I use Escape Rope but my opponent's Active Pokemon has the "Omega Barrier" Ancient Trait does he or she have to switch it? Or if they have a Pokemon with "Omega Barrier" on the bench can he or she choose that and not switch it to Active?
If your opponent has an Active Pokemon with "Omega Barrier", then Escape Rope's effect will be blocked. If a Pokemon with "Omega Barrier" is on the bench, choosing that Pokemon will not stop the effect as the Active was the target of Escape Rope.
Source: Primal Clash FAQ (2015-02-05), TPCi Rules Team (2015-02-05)
Can I attach a Team Flare "Pokemon Tool F" card to my opponent's Pokemon-EX if it has the "Omega Barrier" Ancient Trait?
Yes, you can. The text of Omega Barrier says its effect excludes Pokemon Tools and Stadium cards.
Source: Primal Clash FAQ (2015-02-05), TPCi Rules Team (2015-02-05)