To what extent is water, into which a dead animal has fallen and remained for a period of time, considered pure, knowing that this water is used for ritual bathing (ghusl) and ablution (wudu), and what is the ruling concerning the prayers that were previously performed using this water?

As long as the tanks are large and their water exceeds two qullas, the presence of impurity in them does not cause harm unless one of its characteristics changes (taste, color, smell). Purification with it is valid by the consensus of scholars. However, if the water is less than two qullas, the well-known opinion is that it becomes impure merely by contact with impurity. Nevertheless, one can adopt the view of Imam Malik, which states that a small amount of water does not become impure unless it changes, as Abu Yusuf did when he bathed with water into which a mouse had fallen, and he was unaware of it. Therefore, you are not required to repeat the prayers you performed with this water.