Is it obligatory to repeat prayers missed due to ignorance of the necessity of ghusl from semen or wudu from pre-seminal fluid (madhy) and vaginal discharge? And are the prayers performed with wudu that was invalidated by the emission of discharge considered valid?

If a woman is unsure whether the discharge is semen or something else, she may consider it whatever she wishes (either madhi or normal vaginal discharge). Consequently, she is not required to perform ghusl (definition) unless she is certain it is semen. However, if she is certain that semen was discharged and she did not perform ghusl, or if madhi or vaginal discharge occurred and she did not perform wudu’, then she must make up those prayers that she is certain she performed without purification. If the number is unclear, she should estimate and make up what will achieve certainty or a strong presumption of clearing her responsibility.