Is it necessary to change clothes, wash the body seven times, and perform ablution (wudu') every time one touches a dog to ensure the validity of prayer?

As long as the enquirer is not certain that dog saliva has touched their clothes, the original ruling is that they remain pure. The dog's fur does not defile anything it touches. If they are certain that saliva has touched their body and they wash it seven times, one of them with soap, then their body is purified and their prayer is valid. The Maliki school of thought holds that dog saliva is originally pure, so it is permissible to follow this opinion due to the ease and removal of hardship it offers.