mixture, I
think that you can now legally and officially use a windows 8 sticker in place of a COA, if you fulfil some requirements e.g. UEFI / Secure Boot. This was introduced due to devices with increasingly little "hidden" surface area e.g. tablets, where every side is "for show", and for devices with non-removable batteries.
In this case, the serial number of the machine might indeed be part of the COA.
As for downgrading to W7, I imagine you'd need to speak to MS, probably on the phone, to turn that OEM license into an actual key for W7.
AFAIK only the Pro version has "downgrade rights".