بِسْمِ اللهِ الرَّحْمنِ الرَّحِيْم
In the Name of Allah, the Most Gracious, the Most Merciful.
1) No, the wudu will not break in that case. Water droplet on the tip of the private part is pure.
2) Doubts are not taken into consideration in the Shariah. Doubts should be ignored; otherwise, they will grow stronger and overwhelm you. Yes, if you are certain or you believe most probably it is mazi, then you should wash that area.
3) You should concentrate on the meaning of what you are uttering in salat so that your attention does not go elsewhere. If you are aroused in salat and thereafter you see mazi on the tip of your private part, you have a strong reason to believe that the mazi came out during salat while you were aroused. Hence, you should repeat that salat in this case, as wudu breaks when mazi comes out.
4) The excreta of roosters is impure (napaak). (Hindiya: 1/51, Ilmiyyah)
Regarding the tank water, how did impure water enter it? Give us more details.
Nonetheless, in principle, if tank water does become impure, it will become pure again with two conditions: (1) The tank water becomes “flowing water” (even for a few moments); (2) There are no traces of impurity in the water.
Tank water can become “flowing water” simply by overfilling the tank with water until water overflows from it. Similarly, tank water will become “flowing water” when water enters the tank from one pipe and exits it from another pipe at the same time. (Fatawa Usmani: 1/328; Shami)
And Allah Ta'ala knows best
Mufti Faizal Riza