What is the ruling on the emission of prostatic fluid (madhy) after performing ghusl for janabah and after urinating, and what are the implications of that?

It appears that what comes out after urination is "wady" because it exits following urine. It is impure (najis) and nullifies wudu, requiring purification. If it were "madhy," it would also nullify wudu.

As long as these discharges cease after a period, they do not constitute سلس (incontinence). What you do, placing a tissue and waiting for it to stop, is the ideal solution. If you do not use a tissue, then whatever part of the body and clothing it stained must be washed for prayer.