Abilities » Allergy Panic | Attacks » Shred
If Vileplume's "Allergy Panic" Ability is in effect, does Rayquaza's "Shred" attack consider a Defending Pokemon's weakness as x2 or x4?
Shred isn't affected by "any effects on the Defending Pokemon", but the term "any effects" does not include effects that alter Weakness or Resistance. So in this case the Defending Pokemon's Weakness would be x4 due to Allergy Panic.
Source: TPCi Rules Team (2013-02-28), TPCi Rules Changes Announcement (2017-05-03), TPCi Rules Changes Announcement (2017-05-18)
Abilities » Allergy Panic
If a Pokemon normally has no Weakness, does Vileplume's "Allergy Panic" Ability give it a x4 Weakness instead?
No, if a Pokemon doesn't have Weakness, you cannot *apply* any Weakness multiplier to it at all.
Source: Boundaries Crossed FAQ (2012-11-08), TPCi Rules Team (2012-11-08)
Abilities » Allergy Panic
If I use Cresselia-EX's "Psychic Protection" attack, does Vileplume's "Allergy Panic" Ability override and give it a x4 Weakness instead?
No, since there is no longer a weakness there is nothing for Allergy Panic to multiply.
Source: Boundaries Crossed FAQ (2012-11-08), TPCi Rules Team (2012-11-08)