Issue 1: Wheel rotation

The vehicle does not compute correct wheel rotations. The wheel angular velocity is simply set to a value so that the wheel rotation matches the moving underground. If the wheel is in the air it does not spin correctly.

For a better visual effect you can extend the current code. (Btw, if you have an engine license (indie or pro) you get the vehicle source code for free, so you can easily extend it.) Idea: If the wheel touches the ground without skidding, the current spin is ok. If the wheel is on the ground and skidding (wheel.SkidEnergy > 0) or if it is in the air you could use a higher angular velocity. If the player hits the brakes, you can set the angular velocity to 0 for maximum visual effect.

Issue 2: Braking car moves

The car simulation is only an approximation with some errors and it will sometimes not do what you would expect. Ideas for workarounds:

You might want to remember the vehicle.Chassis.Pose in each frame. And in each frame, if the car was braking and the current vehicle.Chassis.LinearVelocity and AngularVelocity are very low, then simply set the current vehicle.Chassis.Pose to the pose of the old frame.

Or set the friction of the front wheels to zero when you want the car to stop and the front wheels to spin in place.

Yes. See also "Additional Downloads" section at the bottom of the Downloads page.

Since character controllers and vehicles usually need a lot of game-specific tuning and modifications, we give customers the source.