Dualcaster Mage

Dualcaster Mage's triggered ability can target (and copy) any instant or sorcery spell, not just one with targets. It doesn't matter who controls it.

If the copy says that it affects "you," it affects the controller of the copy, not the controller of the original spell. Similarly, if the copy says that it affects an "opponent," it affects an opponent of the copy's controller, not an opponent of the original spell's controller.

If the spell is modal (that is, it says "Choose one —" or the like), the copy will have the same mode. You can't choose a different one.