Will these plug directly into my factory harness?

Yes. The included switch connects to the OEM fog light circuit. If your Prius C originally came with fogs, you're wired already—just swap the old units out. If it didn't, you'll need to run the harness from the switch to the bumper opening, but the connectors are factory-standard.

Do I need to remove the bumper to install these?

No. Access the fog light openings from behind the bumper without full removal. You can work through the wheel well and undercarriage access points. A jack, jack stands, and basic hand tools are all you need.

What if one fog light burns out later?

The bulb is user-replaceable. Access it from the back of the assembly without removing the light itself. Any standard automotive bulb of the correct size works—no proprietary parts required.