Is a woman excused for her mistakes in prayer and ablution due to not seeking knowledge at the beginning of her conversion to Islam, and is she required to make up prayers if she had omitted ghusl after menstruation at the beginning of her prayers?

A Muslim must learn the rulings of his religion. Whoever falls short in this while being able to do so is sinful and must repent and seek forgiveness. As for the prayers you are certain you performed without proper purification, the ruling according to our fatwa (definition) is that they must be made up. If you doubt the validity of a prayer after completing it, do not pay attention to this doubt; for doubt concerning an act of worship after its completion has no effect.