Does Carracosta's "Ancient Custom" Ability negate Stealthy Hood? Or does Stealthy Hood prevent "Ancient Custom" from affecting the Pokemon Stealthy Hood is attached to?
Stealthy Hood prevents Ancient Custom's effect on the Pokemon Stealthy Hood is attached to.
Source: TPCi Rules Team (2020-03-12)
If I use Raichu's "Evoshock" Ability to paralyze my opponent's Active Pokemon, does the Paralyzed status condition get removed if my opponent attaches a Stealthy Hood to that Pokemon on their next turn?
The Evoshock Ability's effect is to Paralyze the opponent's Pokemon; once that Special Condition has been placed it is no longer considered an effect of the Ability at the time your opponent attaches the Stealthy Hood. Therefore, your opponent's Pokemon remains Paralyzed.
Source: TPCi Rules Team (2019-06-06)
Can a Pokemon with an attack that does damage to the opponent's Bench get through Mr. Mime's "Bench Barrier" Ability if the Attacking Pokemon has Stealthy Hood attached?
No, it does not get through. The Bench Barrier Ability is not "being done" to the Attacking Pokemon.
Source: TPCi Rules Team (2019-05-30)
Can I use Lycanroc-GX's "Bloodthirsty Eyes to target an opponent's Pokemon with Stealthy Hood attached?
Bloodthirsty Eyes can target a Benched Pokemon with Stealthy Hood attached, but its effect would be immediately blocked. However, if the Pokemon with Stealthy Hood is Active, Bloodthirsty Eyes can target a Benched Pokemon without a Stealthy Hood and the switch would take place.
Source: TPCi Rules Team (2019-05-30)