How does Avery interact with protective cards?

[SammyMegaBlaziken]

If my opponent plays Avery, and I would otherwise need to discard Benched Pokémon until I have 3 remaining, which of the following would block that effect?
(Most of these questions can be resolved if Avery puts an effect on myself or on my Benched Pokémon.)

If Avery affects my Pokémon in play,
- Leafy Camo Poncho (SIT 160/SIT 214) attached to a Benched VMAX/VSTAR or Sun & Moon Badge (EVS 151) attached to a Pokémon V with Espeon or Umbreon in its name.
- Mysterious Buzz Ability on Benched Ribombee (LOT 146) assuming all my Pokémon in play are Fairy-type and Blizzard Veil Ability on an Articuno (TEU 32) in the Active Spot with all my Benched Pokémon as Water-types,
- Pricness's Curtain Ability on Diancie (ASR 068), assuming all my Benched Pokémon are Basic
- Unnerve Ability on Pyroar (FLI 19), Galvantula (TEU 48), Axew (UNM 154) or Obnoxious Whirring on Vibrava (CEC 109)
etc.

If Avery affects me
- Dew Guard Ability on Milotic (EVS 038)

 

[PokePop]

This reads like a Professor test question.
Here are two rulings from the Compendium that covers both effects that protect Pokemon and effects that protect you:

You searched for Avery - Pokémon Rulings Compendium

View official rulings for the Pokémon Trading Card Game at the Pokémon Rulings Compendium!

compendium.pokegym.net

Let me know if that doesn't clear it up.