Do F1 cars have brake lights?

No. Drivers follow the same line and brake in the same zones so brake lights are not required. 

The red lights on the back of the car are Rain Lights and are required to be sued in wet conditions.

Modern F1F1 is the pinnacle of open wheel,  single seater car racing and arguably the highest level of any motorsport globally.... There's more... cars flash to indicate when the car is harvestingHarvesting refers to the capture and storage of, otherwise lost, energy for use on a flying lap or when needed... There's more... energy from the MGU-KThe MGU-K (Kinetic) harvests energy from the decelerating wheels back to the energy store for later use. The power created... There's more... or MGU-HThe MGU-H (Heat) uses excess exhaust gases from the engine to feed power to the energy store, which is then... There's more.... This is a warning mechanism for approaching cars as a car is slower while harvesting. 

The lights can flash green to indicate that a rookieA rookie is a driver participating in their first season of a particular class. So a driver's first full year... There's more... driverOK, so we all know what the driver is, right. I've always liked the description that F1 drivers are like... There's more... is on track without a full super license.