What must a girl do who neglected obligatory fasting for many years, and broke her fast by engaging in intercourse during Ramadan for three days, and does not know the number of days she missed, and is it permissible for her to feed the poor instead of fasting as expiation for intercourse?

What you broke before puberty does not need to be made up for (qada'), but what you broke after puberty must be made up for. If you do not know the number of days, then exert effort in estimating them. The three days that you invalidated by intercourse must be made up for.

As for the expiation (kaffarah): if you were coerced into intercourse, there is no expiation upon you. If you willingly complied with your husband, then the Shafi'i madhhab and one narration from Ahmad do not obligate expiation upon the woman, and this opinion can be adopted. The majority of scholars obligate expiation upon the compliant woman, which is the freeing of a slave. If you cannot find one, then fasting for two consecutive months for each day. If you are unable to do that, then feeding sixty poor people. It is not permissible to resort to feeding إلا (except) when unable to fast. Regret is a sign of sincere repentance.