You get to redeem 7 past event cards per week. The cooldown timer only starts after you have fully exhausted your redeems.
Your redeems are not carried over to the next week. For example:
If you have 3 redeems left in week 1 you will not receive additional 4 redeems in week 2.
Your redeems are replenished after you have used all redeems and the cooldown timer has ended.