When is ghusl obligatory for a girl who does not recall a wet dream nor find any wetness, but feels a gush of discharge upon rising from bed, or finds a viscous fluid when cleaning herself, and suspects it to be madhy (pre-seminal fluid), or semen, or wady (post-urination discharge)?

A ghusl (ritual bath) is not required due to vaginal discharge. What necessitates ghusl is only semen (maniyy) if it exits with customary pleasure. It has two signs: its smell is like the smell of a man's semen, and one experiences pleasure upon its exit and a decrease in desire thereafter. As for madhiy (pre-seminal fluid), it is a thin, sticky, white fluid that exits when there is desire, but without gushing and without being followed by a decrease in desire. Ghusl is not required because of it. One should turn away from obsessive thoughts (waswasa) and consistently perform the prescribed adhkar (remembrances of Allah), supplicate, and seek refuge with Allah from Satan.