Does something become ritually impure if it touches a seat that was impure with urine, then had water sprinkled on it and dried, then became mixed with other seats such that it cannot be distinguished, and is it obligatory to wash whatever touched any of these seats?

Impurity is not purified by mere sprinkling (nadh), rather it must be thoroughly washed with water so that the impurity is submerged and its substance and traces, such as color or odor, are removed, unless their removal is impossible. So, if sprinkling means washing the impure spot, then it becomes pure; but mere sprinkling does not purify.

If an impure seat is mixed with pure seats, a wet hand does not become impure by touching any of them, because the default state is purity unless impurity is confirmed with certainty. The prescribed approach is to base matters on presuming continuity (istishab): if there is evidence of impurity, then it is ruled impure; otherwise, a thing is not avoided merely due to the possibility of impurity. One should beware of obsessive doubts (waswasa).