Is it obligatory to perform Istinja (washing) or to disregard the emission of a small amount of faeces with wind after defecating and before prayer, knowing for certain that it has been emitted?

You must clean yourself after passing anything from the two private parts if you intend to pray. If the discharge of feces is continuous, either permanently or predominantly, then your ruling is that of a person with incontinence. You should wash the area, tie a cloth over it, and perform ablution for prayer after the time for it has begun. The discharge of anything, even if you are praying, will not harm you. Then, you repeat this for the next obligatory prayer. However, if the discharge of feces stops and it is before the time for the obligatory prayer has elapsed, then you must delay the prayer until it stops, then clean yourself and pray.