Every assignment, quiz and discussion can have due dates, as well as available from and until dates. The latter two would be "opening and closing dates" for the assignments. Please see here for more details on these dates.
I am not sure what you mean by having opening and closing dates for "each week". If you are splitting the weeks by modules and have each module be a week (and that's what you mean by "week"), than the module itself can have an "available from" date, but not an "available until" date, as far as I can tell.
