Do I need to run new wiring, or does it tap into existing power?

The harness connects to your vehicle's existing mirror circuit—no new wire runs needed. Route it along the door frame where the factory harness already sits.

Will this side mirror fit the left side too?

This is a right-side-only assembly. The mounting bracket and internal geometry are specific to the passenger side. You'll need the left-side version for the driver's side.

Does the heater work independently, or only when the engine is running?

The heating element draws power from your vehicle's electrical system—it operates whenever ignition is on and the switch is activated. No engine-running requirement.