Does a debt remain upon the young woman, or is an expiation (kaffarah) obligatory upon her, after she committed some acts in Ramadan out of ignorance of their prohibition and that they invalidate the fast, with doubt about the emission of semen and not remembering the number of days?

Merely looking at pornographic images does not break the fast. Doubting whether an act that breaks the fast occurred does not necessitate making up the fast, because the default assumption is that no act that breaks the fast was committed. As for masturbation, it is among the acts that break the fast if it results in the emission of semen. However, if one performs it out of ignorance that it breaks the fast, their fast is not invalidated. Therefore, the questioner is not required to make up any fasts, and what she has already made up will be considered a voluntary act of worship. It is advised to adhere to obedience to Allah and to abstain from watching forbidden things.