If the card is not played by end of turn, it remains exiled until end of game.

The card is face-up when exiled.

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.

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

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.

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.