If my opponent has Jirachi GX with "Psychic Zone" Ability, does Golurk's "Theta Stop" Ancient Trait bypass "Psychic Zone" and apply Weakness?
Psychic Zone will not be applied to Golurk because of Theta Stop, so any attacks done to Golurk would still apply Weakness. Attacks done by Golurk wouldn't be affected
Source: TPCi Rules Team (2020-03-12)
If a Pokemon with an Ability also has the "Theta Stop" Ancient Trait, would it prevent Wobbuffet's "Bide Barricade" from stopping that Ability?
Yes it would because Bide Barricade is an effect that is targeting the Pokemon, so Theta Stop would prevent Bide Barricade from blocking the Pokemon's Ability.
Source: TPCi Rules Team (2015-09-03)
If Sceptile-EX has its Spirit Link tool attached, but Banette's "Tool Concealment" Ability is in play, what happens if you evolve to Mega Sceptile-EX with the "Theta Stop" Ancient Trait?
Theta Stop prevents the effect of Banette's ability against Mega Sceptile-EX in time for the Spirit Link tool to turn back on and not make you end your turn.
Source: Ancient Origins FAQ (2015-08-13), TPCi Rules Team (2015-08-13)