I'm not sure if I've used it in the rain yet, but my understanding is that, yes, the sensor needs to be kept clean. It follows the SPEED of the car in front of me; I still steer. I assume it uses steering wheel sensors to detect that it should be following the car slightly to the left of me when, say, I'm going around a left-hand curve.

The lane keeping system uses a camera to detect lane markings. I'm not sure how it decides whether or not to follow exits, but I know from the Tesla autopilot descriptions that it's not perfect.