Unfortunately, there is no such thing as an 8-day Park Hopper Pass. There is a 7-day Park Hopper Plus which has 4 Plus Options (for waterparks & Pleasure Island). There are no 7-day Park Hoppers.
The Ultimate Park Hopper (UPH) can be purchased for your length of stay if you are staying on Disney Property. They will cost $381.27 per adult and a child's UPH is $305.66 for 8days/7nights (all prices include tax). UPHs include DQ, PI and the waterparks. They expire at midnight of the day you check out.
If you are considering another visit to WDW within a year of this trip, you may want to consider purchasing annual passes (APs) for everyone. They are $392.99 per adult and $334.41 per child. The APs do not include DQ, PI or the waterparks but you will get a few perks with them including special room rates. They expire 365 days after their first day.
As far as discounts go, you probably will not find any for the UPHs or the APs unless you are a Disney Club member. Other tickets combinations (such as purchasing 2 4-day PHs for each person) will actuall run more than the cost of APs, even if you buy from a discount ticket broker like Ticketmania or MapleLeaf Tickets.