Is it permissible for a non-Muslim (Christian) maid to share the same washing machine with us sequentially, and do the clothes become pure after washing the place of washing with water?

The clothing of a disbeliever is pure unless impurity falls upon it, for their impurity is spiritual, not physical. If their clothing is thought to have become impure due to their lack of precaution regarding impurity, then it is better to avoid it until it is purified.