Do I need a separate amplifier for a car subwoofer?

It depends on the type. Component drivers like the Skar EVL-12 D2 or CT Sounds Bio require a separate amplifier and an enclosure sized to spec. All-in-one options such as the MTX Terminator loaded enclosure (which still needs an amp) or the slim under-seat units with a built-in amplifier are far closer to plug-and-play. If you don't want to deal with box-building or matching amplifier power, a complete package or a powered under-seat sub is the simpler path.