You can click the "reveal triangle" adjacent to your User Account folder — the one shown as "John Appleseed" in that screenshot, and choose among those items to restore.
I would assume that many of the files that were causing my current OS to act very buggy, would be found in the System folder, no?
Not necessarily. Ill-conceived "cleaning" products can corrupt a User Account and the files required to support macOS. The only practicable remedy in that case is to completely erase the Mac and reconfigure it as though it were new.
I understand the confusion you described in your original post, but that's the answer. It is not quite as simple as "old and junk files" as much as it is the destruction such things are capable of. Broadly speaking "old and junk files" are inert. Problems arise when required files become missing or corrupted — a common result of using the aforementioned scam products. They have a tendency to characterize files as "junk" when they are in fact required by the processes that rely upon them. The ill-conceived scam products delete them, and the Mac starts to run poorly. Solution: Erase the Mac. Rebuild it. Don't reinstall the junk.
As Applications, if I import that back, will the applications somehow re-install themselves?
Applications will be restored from the backup, which is not technically considered a "reinstall" — as would be the case with restoring previously installed iPhone's apps originally obtained from the App Store for example.
