Is meat and broth rendered impure if blood gushes out and touches the leg of a sheep, then touches the meat before the hand dries, and will whatever is in the kitchen become impure as a result? And will soap become impure if a wet impure hand touches it? And what should I do about touching damp places like the sink that may be contaminated with soap or impurity? And what is the ruling on things that my mother's hand touched after touching my wet impure clothes, especially if some of them are damp and do not dry, and must the bucket with which I wiped be washed?

The person afflicted with waswas (obsessive doubts) must resist and repel these doubts by ignoring them. Whenever Satan deludes him into believing something is impure, he should base his judgment on the original principle, which is the purity of the thing, unless he is certain of its impurity. There is no harm for someone suffering from waswas in adopting the easier opinion to alleviate burden and hardship. A small amount of impurity is absolutely excused. This is the madhhab (school of thought) of Abu Hanifa, and it was chosen by Shaykh al-Islam Ibn Taymiyyah and preferred by Shaykh al-Uthaymeen. This includes a small amount of impurity from street mud due to the difficulty of guarding against it. All the examples mentioned in the question—if the impurity is present—fall under the category of minor, excused impurities.