What amplifier power does the TS-A250D4 need?

It is rated at 400 W RMS, so an amp delivering roughly 300 to 500 W RMS at the final impedance is a sensible match. Its 74 dB sensitivity means underpowering it will leave output flat.

Can I wire the dual 4-ohm coils to 2 ohms?

Yes. Wiring the two 4-ohm coils in parallel gives a 2-ohm load, and wiring them in series gives 8 ohms. Choose an amp that is stable at your final impedance.

What size enclosure does it work in?

It performs well in a sealed box around 1.0 to 1.25 cubic feet or a ported box around 1.5 cubic feet tuned near 35 Hz. It needs about 5.3 inches of mounting depth.

Is this sub suitable for a shallow space?

No. With a 5.3-inch mounting depth and a large magnet, it needs a conventional box rather than a shallow-mount application.

Does it come with a box or amplifier?

No. It is sold as a bare driver, so you supply the enclosure, amplifier and wiring.

How does it compare with a single 4-ohm 10-inch sub?

The dual 4-ohm coils give more wiring options for matching amplifiers, while a single 4-ohm model is simpler to wire. Output and build are broadly similar in the same class.