Will this plug directly into the factory harness?

Yes. This is a direct replacement lamp—connector matches the OEM housing, so you simply swap out the old unit and plug in the new one.

Does this lamp come with a bulb or is it a complete assembly?

It's a complete assembly with the LED module built in. You're not buying a bulb holder; you're getting the finished light ready to install.

Will the white LED affect my rear wiring or other lights?

No. LED draws less power than halogen and uses the same connector, so there's no load issue or circuit stress. Your factory wiring handles it fine.