Is 800W the real power output?

No. The sustained RMS rating is 220W; 800W and 1200W are peak figures. Expect bass that fills a small cabin, not a competition system.

Will it fit under my car seat?

It is 5 inches deep, 8 inches wide and 10 inches high, so check the gap under your seat first. Power and heated seats often leave less room than manual ones.

Does it work with a factory head unit?

It lists RCA inputs only. Most factory radios have no RCA output, so you would need a line-output converter or a head unit with preamp outputs.

Do I need a separate amplifier?

No. The amplifier is built into the enclosure, so you run power, ground and signal to the unit and mount the remote control up front.

The subwoofer enclosure with built-in amp and the wired remote level control. Wiring kits and mounting hardware are typically not included.

How does it compare with a full-size sub box?

It gives up output and deep bass extension for space. A conventional 10-inch box in the trunk will hit harder, but it takes up room this unit does not.