Running Resolume 6 and 7 at the same time on the same machine is not supported behavior, though you might be able to get it to work.
Resolume 6 and 7 use separate setting folders, so you can have them installed side by side without issues.
Upgrades are discounted.
The price depends on what kind of license for how many computers you'd upgrade to which version.
You can find your upgrade options after logging in to your account and clicking the Upgrade button below your serial number.