Is expiation obligatory for previous, unintentional Umrah mistakes—such as a menstruating woman entering the Sacred Mosque, increasing the number of circuits during Say, and not shortening the hair—knowing that a correct Umrah was completed subsequently?

Menstruation is a sign of puberty, and a menstruating woman is not permitted to enter the mosque. Performing the first 'Umrah while you were an adult and omitting the two pillars of Tawaf and Sa'i due to their invalidity without purity, and your assuming ihram for the second 'Umrah is not valid as long as you are still involved with the incomplete first 'Umrah. If you performed Tawaf and Sa'i in the second 'Umrah, that suffices for the missing Tawaf and Sa'i from the first 'Umrah. Omitting the taqsir (shortening of hair) from the second 'Umrah is compensated by performing it in the third 'Umrah. What you committed of ihram prohibitions before taqsir, out of ignorance, if it was for personal comfort, then there is nothing to be done about it. But if it was an act of destruction, such as shaving or cutting nails, then for each type, there is one fidyah (expiation). The ruling applies to your sister if she omitted taqsir after performing a valid 'Umrah; some scholars hold that delaying taqsir necessitates a dam (slaughtering of an animal).