Is it obligatory to fast for an entire month or offer expiation, and make up the prayers, for one who did not fast the first Ramadan and did not pray in that year due to ignorance of the obligation of fasting and prayer, bearing in mind that he does not remember the number of days he did not fast, and that he fell ill in the last days of Ramadan?

One must make up for missed Ramadan (definition) fasts due to menstruation or other reasons. If the exact number is unknown, one should fast a number that is most likely to clear one's conscience. As for prayer, one should increase supererogatory (nafl) prayers to compensate for any deficiencies in obligatory (fard) prayers, based on the Prophet's (PBUH) saying: "Indeed, the first thing a servant will be called to account for on the Day of Resurrection concerning his deeds is his prayer. If it is sound, he will have succeeded and prospered. If it is corrupt, he will have failed and lost. If there is any deficiency in his obligatory prayers, the Lord, the Exalted and Glorious, will say: 'Look, are there any voluntary prayers for My servant?' Then what was lacking in the obligatory prayers will be completed thereby. Then the rest of his deeds will be dealt with in the same manner."

All Ramadan fasts missed after puberty must be made up, even if the woman was unaware of the obligation, because religious duties are not waived due to ignorance. If she fasted during her menstruation, she must re-fast those days because fasting during menstruation is invalid.