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.
In the term 'days of the week', the nouns 'days' and 'week' are common nouns. The names of the days of the week (Sunday, Monday, Tuesday, etc.) are proper nouns because they are the names of the specific days.
9,000 days is 5 days more than 1285 weeks, so the day of the week in 9000 days will be five days earlier in the week, or two days later in the week, than it is today. As an example, if today is Wednesday it will be Friday in 9,000 days.