Does this need to be wired into my existing brake light circuit?

Yes. This assembly plugs into your factory connector — the same one your original brake light used. If you're replacing an existing unit, the wiring is already in place.

What hardware comes with this to mount it?

The assembly uses your factory mounting points. Confirm your existing fasteners are in good shape before install — you may need to reuse them or source new bolts if corrosion is present.

Will the LED brightness be compatible with my vehicle's brake light circuit?

LEDs draw less current than incandescent bulbs. Your Liberty's electrical system handles this standard — no load resistors or special wiring required for a direct replacement 3rd brake light.