Is the ground on which a dog defecated considered pure after its owner removed the trace, and is soil taken from land with plants suitable for purification, and is the assumption that the excrement was from a dog correct, and is the water that splashed onto clothes while washing shoes impure?

This question arises from waswasa (whispering of Satan/obsessive thoughts), and it is obligatory to avoid waswasa and not pay attention to it.

When in doubt about the impurity of dung, it is ruled to be pure. As long as you are not certain that it is dog dung, and you consider the possibility that it belongs to an animal whose meat is permissible to eat, then it is pure.

Even if you are certain that it belongs to an animal whose meat is not permissible to eat, it is impure. However, it is not definitively ruled to be dog impurity that necessitates purification seven times, one of them with earth.

Dry impurity does not transfer to dry objects, and water separated from impurity during purification is ruled to be pure as long as it has not changed due to the impurity.