What is the ruling on the prayer of one from whom madhiy (pre-seminal fluid) was discharged during its performance, after having purified oneself from it, knowing that she was unable to repeat the prayer before its time expired?

It is forbidden to speak with foreign men, as it may lead to corruption. If you are certain that madhy (pre-seminal fluid) exited during prayer, then the prayer is invalid and must be repeated, as it nullifies ablution. Repeating the Dhuhr prayer is valid, even if the time for Asr began shortly after the takbirat al-ihram (opening takbir); this is because the time for Dhuhr extends until sunset according to some scholars, or you might have caught the takbirat al-ihram and Al-Fatiha within the Dhuhr time. Doubt about the exit of madhy during prayer does not affect its validity, and you should not interrupt the prayer for it, nor is there a need to repeat it; this is because the default assumption is that nothing has exited until proven with certainty, based on the hadith: "He should not leave until he hears a sound or finds a smell."