I looked at the tail/stop lights and they look like they have a bulb in them. The Toyota Prius C product information PDF says they have LED tail/stop lights, so do they or don't they.
The rear turn signals and back up lights are bulbs you can replace. http://www.toyota.com/t3Portal/document/om-s/OM52E68U/pdf/OM52E68U.pdf (page 425 for instructions, Page 498 for wattage and specs)
The updated Cs with the NEW style taillights ( such as yours ) yes. The older ones such as 2014 and below have LED brake lights and incandescent taillights.