What does 4,000W max power mean here?

It is a peak rating. The continuous (RMS) output is 1,000W at 1 ohm, 600W at 2 ohms and 350W at 4 ohms. Plan your subwoofer around the RMS figure.

Can it run at 1 ohm daily?

Yes, it is rated for 1-ohm operation at 1,000W RMS. Running that load pulls heavy current, so check your alternator and wiring before wiring the sub that low.

How much power will I get from a 4-ohm subwoofer?

About 350W RMS into 4 ohms. If you want the full 1,000W, you need a subwoofer or pair of subs that present a 1-ohm load.

Is a Class D monoblock good for subwoofers?

Yes. Class D amps are efficient and run cooler, which suits the continuous low-frequency demand of a subwoofer. The trade-off is that some designs have less headroom than Class AB at the same rating.

What subwoofer should I pair with it?

Match the sub's RMS rating to the amp's output at your final impedance: 350W at 4 ohms, 600W at 2 ohms or 1,000W at 1 ohm. A dual-voice-coil sub lets you pick the load.