What is the ruling on prayers from past years, given the lack of knowledge concerning the rulings on purification from fluids emitted from the private parts, such as semen (mani) and pre-seminal fluid (madhi)? And is it permissible to adopt Ibn Taymiyyah's view that there is no need for making up (qada') in cases of ignorance?

A woman is not required to perform ghusl unless she is certain of the emission of semen, which necessitates ghusl. You must repeat the prayers you performed under the circumstances mentioned.

As for madhy (pre-seminal fluid), its emission necessitates wudu along with washing the part of the body it touched and sprinkling water on the clothes. If you were certain of its emission and did not perform wudu, you must repeat the prayers you performed.

If you performed wudu with the intention of being permissible to pray and did not realize the emission of madhy, that is sufficient for you, and any impurity that touched your body and clothes is excused.

If you are certain that you performed some prayers while you were not in a state of purity, then, according to the majority of scholars, you must repeat these prayers. The making up of these prayers should be according to your ability.

There is no harm in following Sheikh Al-Islam Ibn Taymiyyah's opinion that whoever neglects a condition or pillar of prayer out of ignorance of its obligation is not required to make it up. However, the view of the majority is more cautious and more absolving of responsibility.