Sabbath means "seven" & "rest".
(rest is creation's trait, not creator's)

..which means the last quarter of the month until the crescent moon appears is supposed to be our 7 days of rest. Does a woman's period come every weekend?

The muslims will argue, "What about jumah (friday) prayer?"

All of the days in arabic are named after numbers and friday isn't.

The word "jumah" is only mentioned in verse 62:9. Prophet Muhammad performed his only hajj in his 62nd year and gave his speech on the 9th day of the hajj month. This day is the day of jumah.