What is the ruling on the white discharge that a woman experiences after the end of menstruation? Does it necessitate ghusl if not preceded by a wet dream or lustful thoughts? And what is the ruling on the prayers that the woman performed without performing ghusl, assuming it was natural discharge? Is she obligated to make them up?

The discharge of normal secretions during sleep is not a preventative. If you are unsure whether the discharge is semen or secretion, you may choose to apply the ruling of either. The cure for obsessive thoughts (waswas) is to ignore them and not pay attention to them. Therefore, you are not required to perform ghusl (definition) (ritual bath) unless you are absolutely certain that semen, which necessitates ghusl, has been discharged. Your prayer is valid unless you are certain of that. The discharge of semen during sleep does not require the presence of pleasure or fatigue.