What is the ruling on discharges that come out of a woman, and the surrounding fluid is yellow, and is it obligatory to investigate its ruling upon feeling its descent?

Discharges from vaginal moisture are pure but invalidate ablution (Wudu'). As for yellowish or brownish discharges, they are impure and necessitate purification (Istinja'). You are not required to investigate; rather, act upon the principle that nothing has been discharged. If you are certain that something has been discharged, then if it is a yellowish discharge, perform Istinja' and Wudu'; and if it is from vaginal moisture, Wudu' alone is sufficient for you. Disregard obsessive thoughts.