Is an unknown spray that gets on clothes considered impure, and does the mosque carpet become impure by contact with clothes wet from this spray?

The impurity was removed by washing it the first time, and no more than that is required. In fact, washing was not required at all, because a thing does not become impure through doubt. Therefore, these whisperings (waswas) must be dismissed. If the matter is one of waswas, it is advisable to persevere in supplication and humility, to ignore the whisperings, and to consult a trustworthy psychiatrist.