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 F1 cars flash to indicate when the car is harvesting energy from the MGU-K or MGU-H. This is a warning mechanism for approaching cars as a car is slower while harvesting.
The lights can flash green to indicate that a rookie driver is on track without a full super license.
[caption id="attachment_7508" align="aligncenter" width="736"] Rear lights : beyondtheflag.com[/caption]