Is ammonia solution ritually pure (tahir), and is a woman's prayer permissible if her hair is dyed with a dye containing it, especially given that its smell resembles the smell of cat feces?

The ruling on prayer in the presence of ammonia varies depending on its source. If it results from the chemical reaction of gases (nitrogen and hydrogen), it is pure, as the default state of things is purity. However, if it results from impure organic fertilizer, such as human or non-halal (definition) animal waste, it is impure. If it comes from the waste of a halal animal, it is pure. Its ruling can be determined by asking experts or by reading its components on the packaging.