What is the ruling regarding the prayer I performed after washing away discharges, where it became apparent that there were a few residual discharges that were not completely removed during the washing, along with not remembering the specific prayer in question?

These discharges are the natural secretions of a woman's vagina, and they are pure according to the preponderant opinion, and do not necessitate ablution (Istinja'). The persistence of some of their traces does no harm. However, if they were madhy (pre-seminal fluid) or an impurity, your prayer is valid and you are not required to repeat it due to your ignorance of the impurity's presence. For avoiding impurity is a condition when one is aware and capable.