Must a woman perform ghusl if, after sleep, fluid is discharged while relieving herself, and she doubts whether it is semen due to inability to distinguish it, given that she only performed wudu when in doubt? And must she ascertain the time the fluid was discharged?

A woman must examine the characteristics of the discharge to treat it according to what is legally required. If she is uncertain about the matter, she should choose the ruling of one of the possibilities she is unsure about. So, if she doubts whether it is mani (seminal fluid) or vaginal discharge, and she chooses to consider it vaginal discharge and suffices with wudu (ablution), then her action is correct.