Can I resolve this effect that has been destroyed, banished, or sent to the deck?

Question

Scenario 1:

I activate "XYZ Effect". My opponent activates Mystical Space Typhoon. XYZ Effect is destroyed. Does XYZ Effect resolve?

Scenario 2:

I activate "XYZ Effect". My opponent activates Cosmic Cyclone. XYZ Effect is banished after he pays 1000LP. Is "XYZ Effect" resolved?

Scenario 3:

I activate "XYZ Effect" My opponent activates a card that returns my card to the deck. Is "XYZ Effect" activated?

Answer 1

Does XYZ Effect resolve?

In all scenarios you mention XYZ Effect resolves

Why? Because neither MST, Cosmic Cyclone, or that card that returns to deck have the ability to negate effects; they "just" destroy the card, but never negated its activation and thus it resolves.

This situation is similar to one answer I gave recently. The only cases where a card like MST or similar (that just destroys) can prevent a spell/trap card effect from activating is if that spell/trap card has a continuous effect.

For example, if your opponent activates Fire Formation - Tenki and you cast MST on it your opponent will not be able to search for a beast-warrior. This is because cards with continuous effects must remain face-up on the field to resolve their effects.