Unless you have space issues, I would recommend letting the Cyberlink Application manager decide where to put the software and the templates. That is the most easy and secure way of working. If you have a space issue on your system disk (usually C: ), I would recommend looking for a larger C:-drive, since you are reorganizing your PC as it is.
And I would never “install” install programs on a freshly installed Windows computer by running a restore. That will not work, or not work in the end. Use the normal installation procedures.
To storage of your video and image files is, I think a personal matter. It depends a bit how much you have and how (regularly) you use them. Many have to storage done by date. And set some extra flags to identify (special) events. And depending on usage frequency and amount you may want to use (additional) external drives too.
If you done have too much medica files, you may decide to keep them on an internal disk per event or sorted on date. There are programs out there that help you find the files back, and even windows Movies and Photo's can help you with that.

If possible I would avoid using the system drive (C:-disk) for the long-during storage of your media files. This helps you having space for programs, and temporary files (even those generated by PD, like the shadow files), and (downloaded) templates etc.
I would recommend to using internal drives to hold the media files of a project during the editing at least. And also depending on the importance of the project and whether you expect to be reusing and/or reediting the project, I would recommend to pack the project materials when you are done in a separate folder, that can easily be retrieved (even if you put it away on a backup external drive), and you are sure that all project material will be there.

Quote Unless you have space issues, I would recommend letting the Cyberlink Application manager decide where to put the software and the templates. That is the most easy and secure way of working. If you have a space issue on your system disk (usually C: ), I would recommend looking for a larger C:-drive, since you are reorganizing your PC as it is.
And I would never “install” install programs on a freshly installed Windows computer by running a restore. That will not work, or not work in the end. Use the normal installation procedures.

I'm sorry, I should have said that I used CAM to install the software, and installed on C. It sounds like those were good choices.

Quote I would recommend to using internal drives to hold the media files of a project during the editing at least. And also depending on the importance of the project and whether you expect to be reusing and/or reediting the project, I would recommend to pack the project materials when you are done in a separate folder, that can easily be retrieved (even if you put it away on a backup external drive), and you are sure that all project material will be there.

With my restored files now sitting on the internal SSD in a folder called Volume{1277c657-e66b-4d34-aa66-8c03fa0e9b41}, I'm concerned about existing projects and getting them in the correct spot to avoid messing them up. I packed my most recent projects, so there's no trouble there. However, my older projects I didn't pack. Do you know what will happen if I just put them exactly where they were before?

Warry covered what needs to be done pretty well. You can go ahead and restore the backup as is. The Drive C 128 GB ssd is too small for anything other than Windows and a few programs. Afterwards you can move the allowed folders like the users Documents, Downloads, Music, Pictures, and Videos folder over to the internal D 1 TB drive to gain more free space on the Drive C if desired. Nothing wrong with browsing for assets on a project. I usually only need to browse once to cover all missing assets since they are usually in one folder.

In Windows 10, I had to disable the default One Drive backup to accomplish this so this may not be for you.