Was what I saw madhiy (prostatic fluid)? What is the ruling on prayer if the entire male organ is not washed from madhiy? Is wudu’ (ablution) required after madhiy exits for one who was already in a state of wudu’? Is it obligatory to repeat istinja’ (washing of private parts) after sprinkling the inner garment with water?

If you are certain that a drop of madhy (pre-seminal fluid) has exited, then what you did by washing the tip of the penis is correct. Washing the entire penis and testicles is not required according to the majority of scholars. Sprinkling water on clothes is not obligatory unless madhy has stained them, in which case only the affected area should be sprinkled. The emission of madhy does not necessitate wudu' (ablution) unless you intend to pray or perform something for which wudu' is a prerequisite. If you are uncertain whether it is mani (seminal fluid) or madhy, you may choose between them. Ignore intrusive thoughts (waswasa) as indulging them leads to great evil.