Is the fasting valid for a girl who fasted while believing that she was not required to fast after the appearance of pubic hair before puberty, and is she required to make up the days she missed in Ramadan after the current Ramadan or before it, and is expiation due if she delays making up the days until after the next Ramadan?

The mentioned sign is a sign of puberty. The questioner must make up the days of Ramadan she missed after reaching puberty. If she does not know their number, she should make her best estimate until she is certain or highly confident that her obligation has been fulfilled. As for what was fasted in Ramadan with the belief that fasting was not obligatory, it is not necessary to make it up, because the intention of obligation is not a condition for fasting. Along with making up the fasts, a expiatory feeding of a needy person is required for each day whose makeup was delayed without a valid excuse. However, if the questioner was ignorant of the impermissibility of delaying the makeup, then no expiatory feeding is due upon her.