Is it obligatory to repeat the prayer if one passes wind or urinates uncontrollably during it? Is it permissible to pray in such a state without repeating the prayer? Is it possible to prolong the prayer and supplication therein while wind continues to pass? Is it necessary to repeat ablution for every two rak'ahs in Tarawih and Qiyam al-Layl prayers when experiencing urinary incontinence?

If you suffer from continuous flatulence and urine leakage, then all you have to do is perform ablution for each prayer after its time has begun, and pray the obligatory and supererogatory prayers. What exits during ablution or prayer does not harm you, and you are not required to repeat the prayer. The cessation of flatulence is not taken into consideration if it is not regular and causes hardship, as Ibn Qudamah mentioned concerning the ruling on a woman with irregular bleeding, for the detailed examination of cessation is difficult, and the Sacred Law did not intend it. This applies to the Tarawih prayer and the night vigil prayer, so you are not required to repeat ablution after every two salutations.