Can you chain breaker the magical warrior's effect to torrential tribute?

Answer 1

In either scenario below, whether he was summoned or on the field, his effect will not do anything to prevent Torrential Tribute's effect, in fact, Breaker can't chain his effect to Torrential in the first place. The only way that Breaker can win against Torrential Tribute is when his already on the field and you destroy it when its face down before it could activate its effects. Lets put this in scenarios.

Scenario 1 - Normal Summoning Breaker

1. You Normal Summon Breaker the Magical Warrior

2. Breaker's effect activates to gain 1 spell counter (Chain 1)

3. Your opponent chains Torrential Tribute to Breaker's summon (Chain 2)

4. Chain resolves backwards which Torrential Tribute (chain 2) destroys all monsters on the field, then, Breaker's effect (chain 1) goes off. However, since Breaker was destroyed by Torrential Tribute and his effect doesn't have its designated target (himself) to put a spell counter on, his effect cannot happen so nothing happens for chain 1.

Scenario 2 - His on the field the field

Lets say his on the field with one spell counter, you summon a monster and your opponent activates Torrential Tribute in response to the summoning. Firstly, during this time, you cannot use Breaker's effect on Torrential Tribute since his Spell/Trap Destruction effect is an Ignition effect, which means effects that require a manual activation by the card's controller usually during their own Main Phase 1 or 2. To start things off, most Ignition effect during a chain would most likely be the first effect during a chain (chain 1), if it isn't on the chain then Ignition effects cannot activate their effects in response to the cards in the chain. While he has an Ignition effect, his effect is Spell Speed 1 (which all Ignition Effects are), while Normal Traps (which torrential Tribute is) are Spell Speed 2, you cannot use an effect to chain to something that has a faster Spell Speed than a card that has a lower Spell Speed. If he could chain his effect to Torrential Tribute, his effect needs to be a Quick effect, which is a Spell Speed 2 and at par with Traps in order to successfully chain his effect to it. So after that all that trouble, Torrential Tribute activates, all monsters are destroyed without Breaker activating his effect.

PS - Even if you were going to use Breaker's effect in response to Torrential Tribute (which you can't as stated before), you would destroy Torrential Tribute but its effects will still go through and proceeds on to destroy all monsters, regardless if it was not on the field. The only way on stopping any card effects completely is when you have cards that can negate certain effects, for example, Dark Bribe, Solemn Judgment, Divine Wrath etc.

Lets make this into a scenario

1. You summoned a monster(s) with whatever effect or Normal Summon

2. Your opponent responds your summon(s) with a Torrential Tribute (chain 1)

3. You use Breaker's effect in response to Torrential Tribute (chain 2)

4. Chain resolves backwards which Breaker's effect (chain 2) destroys Torrential Tribute, then, Torrential Tribute's effect (chain 1) goes through and proceeds on destroying all monsters.

Hopefully this helps you know that Breaker can't use his effect to chain to Traps in general and sorry for the long explanation and possibilities but that's how the gameplay and rules for Yu-Gi-Oh! works.