For example, does Guitar Rig 7 depend on Guitar Rig 5 and/or 6 and, if not, can I just delete them for more storage space?
No, in general newer versions don't need the older versions installed unless you've used the older versions in projects. If you have projects using the VST3 version of GR6 depending on the DAW they may auto-migrate to the latest version.
Yep. Just as long as these are not part of older projects. Remember that GR7 won’t auto replace an old instance of GR6 in a project.
VP