Mind's Desire

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.