The lights in this game are baffling, especially what they do to the road surfaces at night.
That nonsense aside, the headlights do cast shadows, but only the stock car headlights. The additional mounted rally lights do not, and overpower the normal headlights with their extra brightness and throw, so you only see the stock headlights' shadows a short distance from the car and on the sides as you pass very close to objects where the mounted lights aren't overtaking the normal headlights. Like this: https://i.imgur.com/4yu4alb.mp4
These shadows still no doubt hit performance, but you can't even really see them most of the time, so the game is just wasting performance rendering dynamic shadows that are essentially unnecessary. Worst of both worlds! I have to wonder if the devs are even aware of this at all.
They should flip them so the mounted lights cast shadows instead, or just disable all of the headlight dynamic shadows so performance isn't being reduced by a shadow effect you can barely even notice unless you slow down and drive very close to something to see them on the fringes. It's ridiculous.
As for brake lights, I'm not sure what car it was but I noticed that as well in a replay a while back - except the brake lights were working, they were just incredibly dim and at a distance looked like they weren't kicking on despite being visible at the proper levels of brightness in the reflections on the surface. It still looked weird/broken of course and should be investigated.