1. You want to restore the FTM 2006/16 file. This file has all of your media stored inside the file. So, if you want to keep photos or census record images linked directly to a person, you have to do it from this file.
2. FTM 16 runs just fine in Windows 7. I use it every day. There are a couple of minor conflicts, but they will not effect trying to restore the file.
3. Make a list of every copy of this file that you have, both on your computer and on Carbonite. Put that list in a message here, including Name, File Extension, and size. You will probably have to work at this, including calling Carbonite and fussing at them. When I found out that I couldn't identify or restore individual files from Carbonite about a year ago, I cancelled my subscription and went to a different backup source.
4. Step 4 will depend on the answers to step 3, so get us that info, and we'll move forward.