What is the ruling on making up prayers missed for years due to performing tayammum, despite being able to perform wudu, out of ignorance on her part, and is it permissible for her to pray Tarawih if making up prayers is obligatory upon her?

Purity is a condition for the validity of prayer. Tayammum (definition) is resorted to only when water cannot be used, such as when it is absent or when its use would cause definite or probable harm. Whoever performs tayammum while being able to perform wudu has an invalid prayer and must make it up. Therefore, the questioner must make up all the prayers for which she performed tayammum while being able to perform wudu. She is permitted to perform Tarawih prayer and other restricted supererogatory prayers, but not unrestricted ones. Some Malikis are of the view that one who has missed prayers should not perform any supererogatory prayers at all.