If I use Umbreon's "Feint Attack" on an opponent's benched Charizard ex, would the damage be blocked by Charizard ex's "Tera" trait or would it go through since "Feint Attack" ignores all effects on the opposing Pokemon?
Tera traits are considered effects on that Pokemon, so Feint Attack would get through it.
Source: TPCi Rules Team (2024-01-04)
If my opponent has Arcanine ex or Gyarados ex on the Bench, will its "Tera" attribute prevent me from placing damage counters on it with Drifblim's "Curse Spreading" attack?
No, placing damage counters is different than dealing damage, so it won't be prevented.
Source: Scarlet & Violet FAQ; TPCi Rules Team (2023-03-30)