Is the water that comes out of the male organ after cleaning water has entered it considered to nullify ablution, and are the prayers performed with this ablution valid?

It is sufficient for istinja' to wipe the private part with a tissue or to wash it with water. If urine spreads to more than the glans, then washing with water becomes obligatory. Washing the outer part of the private part with water is sufficient, and it is not prescribed to introduce water inside. Any wetness remaining from the water on the area of istinja' is not considered impure nor does it nullify wudu' unless it enters the urethra and then exits. If water enters inside the penis and then exits, then it is considered impure and nullifies wudu'.

As for one afflicted with waswas (obsessive whispering), he must disregard anything he considers to be extraneous after istinja', and he is not required to repeat wudu' or prayer. It is recommended for the one afflicted with waswas to sprinkle water on his private parts and trousers to cut off the waswas.