What is the ruling on water that comes out a short while after performing istinja (washing after using the toilet), or when sneezing or coughing forcefully? Is it urine, water from istinja, or a discharge?

Normal secretions (vaginal discharge) are pure and invalidate ablution (Wudu'), but they do not necessitate Istinja' (washing the private parts). As for urine drops, if you are certain they have come out, then Istinja' and Wudu' are required for prayer. If they are continuous, wait until they stop, then perform Wudu' and pray.