What should a girl do to make up for 300 days or more of missed fasting, and is feeding [the poor] sufficient as a substitute for fasting, and if permissible, can the food be given in installments?

It is not permissible to suffice with feeding [the poor]; rather, it is obligatory to make up all the days missed in Ramadan, whether with an excuse or without one. The make-up must be performed according to one's capacity and in a way that does not cause harm. If you are unable to make up [the days] this year, then complete them in the coming years. Along with making up [the days], a expiatory feeding (fidyah) of a poor person for each day whose make-up was delayed is obligatory, unless you were ignorant of the impermissibility of the delay, in which case there is no fidyah upon you.