Both "what days of the week" and "which days of the week" are correct; however, "which days of the week" is typically used when the choices are limited, while "what days of the week" is more open-ended.

Seven days in a week is more generally used than seven days in the week, except if in reference to a specific week such as 'the seven days in the week' when referring to a specific week, such as the week before Christmas.

There are 7 days in a week and there is 4 weeks in a month

5 days is one work week, but there are 7 days in a week.

There are seven days in a week.