How does a woman distinguish between what is emitted from her—whether it be mani, madhi, wadi, or discharge—without doubt or waswasa (Satanic whisperings)? And what is the proof that madhi and wadi are emitted from women and not exclusively from men?

The default is for things to remain in their original state until certainty of the contrary is achieved. So, whoever doubts that something has exited from them should not pay attention to the doubt, because indulging in whispers (waswas) leads to great evil. Allah holds His servants accountable for their actions according to the Sharia (definition), not for what is in reality. To distinguish between mani (spermatic fluid) and madhi (pre-seminal fluid), the characteristics of each are known. If a woman cannot distinguish between what has exited from her, she should choose and assign it the ruling of one of them. This is more lenient for those afflicted with waswas.