Do F1 cars have brake lights?

Answer 1

No, they don't. Braking at the last possible moment before the turn can be a big benefit for the driver, especially on technical tracks (short straights, lots of turns), and indicating this would give the advantage to the trailing car's driver. The F1 car is, however, equipped with light at the back, which is only switched on during poor weather conditions or when the pit lane speed limiter is on.