Is the 1,000W rating real continuous power?

No. The 1,000W is a peak max-power figure. Continuous RMS output is 120W x 2 at 4 ohms, 200W x 2 at 2 ohms, or 400W x 1 bridged at 4 ohms.

Can it run two speakers and a subwoofer?

Not at once. It has two channels, so you can drive two speakers, or bridge the channels into one subwoofer, but not both together.

Does it work with 2-ohm speakers?

Yes. Each channel is rated for 2-ohm loads at 200W RMS, so 2-ohm speakers and dual-voice-coil subs wired to 2 ohms per channel are supported.

Class A/B or Class D for a car?

Class A/B, like this amp, is simpler and often cheaper but less efficient and runs hotter. Class D amps are smaller and cooler but usually cost more for the same output.

What do I need to install it?

A fused power wire from the battery, a ground, remote turn-on, RCA inputs and speaker wiring. Plan for ventilation since Class A/B amps generate heat.