“Amsakā” is a third-person dual masculine past-tense verb. Its dual subject suffix refers to the two people named earlier: the traveller and the menstruating woman. Arabic commonly uses the masculine dual for a mixed-gender pair.
“ʿAn al-ṭaʿām wa-l-sharāb” is a prepositional phrase; “baqiyyata yawmihimā” specifies the rest of their day.