The copies are put directly onto the stack. They aren't cast and won't be counted by other spells with storm cast later in the turn.

Spells cast from zones other than a player's hand and spells that were countered or otherwise failed to resolve are counted by the storm ability.

A copy of a spell can be countered like any other spell, but it must be countered individually. Countering a spell with storm won't affect the copies.

The triggered ability that creates the copies can itself be countered by anything that can counter a triggered ability. If it is countered, no copies will be put onto the stack.

You may choose new targets for any of the copies. You can make different choices for each copy.

If the enchanted creature gains an ability after Amphibian Downpour becomes attached to it, it will keep that ability.

Amphibian Downpour overwrites all colors and creature types the enchanted creature has. It's just a blue Frog. The creature keeps any supertypes it has (such as legendary) but loses any other card types it has (such as artifact).

If the enchanted creature has any subtypes other than creature types, such as Equipment, Vehicle, or Urza's, it loses those as well.

Amphibian Downpour overwrites all previous effects that set the creature's base power and toughness to specific values. Any power- or toughness-setting effects that start to apply afterward will overwrite this effect.

Effects that modify the creature's power and/or toughness, such as the effect of Wing It, will apply to the creature no matter when they started to take effect. The same is true for counters that change its power and/or toughness and effects that switch its power and toughness.

Amphibian Downpour may enchant a permanent that is only temporarily a creature, such as a Vehicle. If this happens, Amphibian Downpour's effect causes the enchanted permanent to remain a 1/1 blue Frog creature even after the temporary effect making it a creature expires.

Because damage remains marked on a creature until the damage is removed as the turn ends, nonlethal damage dealt to a creature may become lethal if Amphibian Downpour becomes attached to it during that turn.