Check the wiring harness connections in the passenger footwell - my car was missing the felt cover that goes over them, and a passenger kicked one of them loose. Brake warning came on, turn signal stuck on, car went nuts.
One time I had similar situation, when drove the "S" curved road. Something happened, turns were not working, wipers going wild. I also had problems with ABS system.
I cleaned the connections in passenger footwell - like @lunalolvo said. Weird situations didn't come back again. Do this with electric cleaner and brush - should be fine. You have to pull out whole CEM.