Gargos's controller chooses which creature (if any) Gargos will fight, not the controller of the spell.

Gargos's cost-reduction ability affects only generic mana in a Hydra's cost. For example, if you cast a Hydra spell with mana cost {2}{G}{G}{G}, it will cost {G}{G}{G} to cast, not {G}.

If the target creature is an illegal target when Gargos's last ability tries to resolve, the ability doesn't resolve. If Gargos is no longer on the battlefield, the target creature won't deal or be dealt damage.

To determine the total cost of a spell, start with the mana cost or alternative cost you're paying, add any cost increases, then apply any cost reductions (such as that of Gargos). The mana value of the spell remains unchanged, no matter what the total cost to cast it was.

If a spell has {X} in its mana cost, you choose the value for X before applying cost reductions. For example, if you cast a Hydra spell with mana cost {X}{G}{G} and choose for X to be 6, you pay {2}{G}{G}. Any of that Hydra's abilities that refer to X still uses 6 as the value for X regardless of what you actually paid.

Gargos's triggered ability resolves before the spell that caused it to trigger. It resolves even if that spell is countered.

If a spell targets one creature you control multiple times, Gargos's ability triggers once. If that spell targets multiple creatures you control, Gargos's ability triggers once for each of those creatures.

Gargos's cost-reduction ability applies only while it's on the battlefield. Gargos doesn't reduce its own cost.