What is the ruling on the prayers of one who has performed ghusl from menstruation for years without washing her hair, believing her action to be correct, and must she repeat them?

If the reality is as you described, then you must repeat the prayers you performed with that ghusl, as long as you knew that washing the hair is obligatory. Even if you neglected to wash it out of ignorance, you are still required to repeat them according to the majority of scholars, because ghusl is not valid if the hair is not washed. And if ghusl is not valid, then the purification, which is a condition for the validity of prayer, is not achieved.

Some jurists have held that whoever violates a condition of prayer out of ignorance is not required to repeat the prayer, but the opinion of the majority is more cautious.

If you do not know the number of those prayers, then strive to estimate their number and pray what you believe most likely clears your conscience.