What is the ruling regarding the prayers performed by the questioner for six months in the opposite direction of the Qibla, assuming it was the correct direction, and is she required to make them up, and how is that done? And is it obligatory to make up the prayers she missed during adolescence despite her repentance?

Whoever makes a mistake in facing the Qibla while in a city must repeat the prayer unconditionally, because they have access to mihrabs (prayer niches) and established Qibla directions, and they can find someone to inform them with certainty. They are obligated to make up all those prayers. As for prayers missed before puberty, there is no making up for them. Regarding prayers missed after puberty, there is a difference of opinion on the obligation to make them up. However, it is more cautious to make them up, in agreement with the majority of scholars and to avoid disagreement.