Nothing in your house should be deemed impure unless you know for certain that this man touched it, and that his hands were still wet when he touched it and the dog’s saliva had not yet dried up, or he touched something wet when there was still a trace of saliva on his hands. For more details, please see the long answer.

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.

One cannot pray in impure clothes because of the general meaning of the texts which indicate that clothes should be pure when praying. They do not differentiate between dry impurity and wet impurity. Impurity cannot be removed from a garment except by washing it with purifying water. It is not sufficient merely to let the impurity dry out.