The Mountain will remain a creature for the rest of the game. It doesn't have a creature type.

A noncreature permanent that turns into a creature can attack, and its abilities can be activated, only if its controller has continuously controlled that permanent since the beginning of their most recent turn. It doesn't matter how long the permanent has been a creature.

As the replicate triggered ability resolves, you'll copy Shattering Spree for each time you paid its replicate cost, even if the original spell is no longer on the stack at that time (perhaps because it was countered).

The copies that replicate creates are created on the stack, so they're not "cast." Abilities that trigger when a player casts a spell won't trigger.