1. I know the expression 'go to the movies'. Then, 'go to the pictures' means go to the art gallery or something?-- No. 'Pictures' = 'movies'.
2. I don't know why 'in the car' is used. Can't I say 'She used to go to the pictures 'by car' or 'with her car'?-- 'By car' might be OK unless the context makes the car more prominent in some way. 'With her car' is no improvement.