Erm, dual boot is dual boot... i.e. everything segregated, no shared files. If you're seeing shared files then you've not done something right (unless you've mounted and are browsing the unbooted partition).
Oh, a quick aside: Is it better to download a new OS ISO - i.e., will it be more up to date while still accepting the old key?
Yes. Newer ISOs typically have SP's slipstreamed so its a good thing and saves you downloading it later.