Is it permissible for the person afflicted with سلس البول (urinary incontinence) to perform istinja (washing of private parts) before the prayer time begins, and then perform wudu (ablution) after the prayer time has begun, or must he perform istinja and wudu after the prayer time has begun? And must he re-pray the prayers that were performed with istinja done a few minutes before the time?

The validity of your ablution (wudu) and the prayers (salat) performed with it depends on the ruling concerning the continuity (muwalat) between Istinja (cleaning oneself after relieving oneself) and wudu. Some scholars, like the Shafi'is, stipulate continuity between Istinja, wudu, and prayer for someone afflicted with urinary incontinence ( سلس البول - سلس البول), but they exclude flatulence (سلس الريح) from this ruling. In contrast, some scholars are of the opinion that a person afflicted with incontinence is not required to renew Istinja or to bandage ( التعصيب ) for every prayer. Meanwhile, the Malikis hold that a person with incontinence is not obliged to perform wudu for every prayer, nor to wash the place of impurity. Based on this, your prayer is valid according to the view of the Hanbalis and Malikis, and there is no need to repeat it.