Do I need any additional wiring or relays?

The harness and switch come integrated, so no extra relay is needed. Plug the connector into your vehicle's existing fog light circuit if equipped, or wire directly to a 12V source with proper fusing.

Will this work if my vehicle didn't come with factory fog lights?

These are designed for the factory fog light location. If your Corolla has no factory opening, test-fit before committing to installation. Existing body structure will determine feasibility.

Can I replace just the bulb later?

Yes. H11 bulbs are standard and widely available. You can swap the bulb at any time without removing the entire assembly.