Is it obligatory to repeat the prayer if there is a remaining adhesive patch preventing water from reaching the skin after performing wudu? And is it obligatory to repeat it if clear fluid—pre-seminal fluid (madhy) or prostatic fluid (wady)—is discharged during prayer?

Wudu' is not valid if there is an adhesive on the limb because it prevents water from reaching the skin, which is a condition for the validity of wudu'. This invalidates both wudu' and prayer, unless the barrier is very minimal, in which case some scholars excuse it. However, it is more cautious to repeat the prayer and wudu', as the majority of scholars do not consider purification valid with any barrier, even a minimal one.