The mere fact that a dog passed through a place does not render it impure.

Following the Prophet’s guidance, the impurity of a dog is to be removed by washing the vessel seven times, one of which should be with soil.

If speaking in the bathroom happens when one is relieving oneself, it is not allowed, and it is contrary to good manners and dignity. As for speaking in the bathroom at a time other than when relieving oneself, there is no text to indicate that it is not allowed.