What is the nature of the fluid that exits after urination or during defecation, without pleasure or orgasm, and sometimes continues to flow for minutes? Is it maniy or wadiy? And is it obligatory to repeat ablution or prayer if it exits after ablution or during prayer without any lustful thought?

The liquid that appears after urination is "al-wady," and it is impure (najis). Its ruling is the same as that of urine. The body and clothes must be purified from it. It does not necessitate ghusl (definition) (full ritual bath), but only wudu (ablution). If it appears after wudu, it invalidates it, and prayer is not valid except by renewing wudu; otherwise, the prayer is void and must be repeated.