Silverquill, the Disputant

Casualty N means "As an additional cost to cast this spell, you may sacrifice a creature with power N or greater." and "When you cast this spell, if a casualty cost was paid for it, copy it. If the spell has any targets, you may choose new targets for the copy."

The copy of the spell is created on the stack, so it's not "cast." Abilities that trigger when a player casts a spell won't trigger.

If you pay the casualty cost of a spell, the copy will resolve before the original spell.