Should we refrain from seeking knowledge from a student of knowledge who is well-versed in knowledge and encourages piety and adherence to the Sunnah, after learning from a woman that he had an illicit secret relationship with her, or should we consider that every human makes mistakes and he might have been overcome by this sin?

No human is infallible, but a pious Muslim must remember and recognize his sin when he commits it, and repent and seek Allah's forgiveness. This student who teaches women should have remembered that he is entrusted with teaching women and that he should not be a wolf among them, and that he should close the door to fitna (temptation/strife) for himself and others. As the Messenger of Allah, peace and blessings be upon him, said: "I have not left behind me any fitna more harmful to men than women." You must cut ties with this lesson, and you can make up for what you missed with lessons from trustworthy scholars. You should also advise your friend to cut ties with this student, and both of them should repent to Allah the Almighty. A message should be conveyed to this student that he should stop teaching women altogether.