The Romans did not have the same days of the week as we did. They did have the same number of days per month, roughly, but they counted their days as a # of days before 3 named days each month. For example, the first of the month was the "Calends" and you would refer to they day of the 'week' as 'two calends of January' which would be two days before January 1st for us. The Ides, is another one of these named days of the month and you'd tell what day it was in relation to the Ides. The Ides was the 13th or 15th of the month depending if it was a long or short month. Then there was also the Nones which was either the 7th or 5th.

More specifically to the question of when we started using Monday-Sunday as days of the week--I don't know.

See 'SPQR' by Mary Beard.

Edited for typos.

What about other calendars, like how long have the Jewish Sabbath lined up with the current one?