Unnerving Assault affects only creatures on the battlefield at the time it resolves. If a creature enters later that turn, it won't be affected.

The spell cares about what mana was spent to pay its total cost, not just what mana was spent to pay the hybrid part of its cost.

If a creature changes controllers later in the turn, that won't change how Unnerving Assault affected it.

If the spell is copied, the copy will never have had mana of the stated color paid for it, no matter what colors were spent on the original spell.

The spell checks on resolution to see if any mana of the stated colors was spent to pay its cost. If so, it doesn't matter how much mana of that color was spent.