Is it necessary to wash the private parts with water after the discharge of vaginal fluids before performing ablution (Wudu), and does the ruling differ if the cause was sexual intercourse or a wet dream?

Vaginal discharge is pure according to the preponderant opinion, so istinja' (cleansing after urination/defecation) is not obligatory for it, nor is washing what has touched the body or clothing from it. As for madhiy (pre-seminal fluid), it is impure, and istinja' from it is obligatory, as is purifying what has touched the body and clothing, and performing wudu' for prayer. If you doubt whether the discharge is madhiy or vaginal discharge, you may assign to it the ruling you wish. If you doubt whether anything exited at all, the default is that nothing exited, so you are not required to repeat wudu'. In cases of ambiguity, follow the scholar whose knowledge and piety you trust, and there is no sin upon you if you do so.