Seagate backup does not cover installed apps. It backs up the data created by the apps and probably also Windows settings, favorites and the stuff on your desktop like folders and shortcuts. Apps cannot be "backed up" unless they are standalone simple executable files. They must be installed. When programs ("apps") install themselves they put information in the Windows registry and deposit files in various places that comprise the operating system structure - things that cannot be duplicated in backups, not by Seagate or any other backup product. "Backing up" is for saving data, not installed apps.
During the restore process it sounds like you must have told the installer to delete the existing partitions and and so it created new ones without the apps and data.
I can't tell from post #24 if you are saying you did another fresh, clean install of Windows subsequent to the restore you talk about in post #22 or if you are continuing on with the result you describe in post #22. What about the problem with the full drive? Is that still an issue? If you have lost your apps and data anyway, I think your next move should be to do a fresh clean from scratch install of Windows (including deleting the existing partitions) unless you have already done so.
Concerning your slow internet speed, are you connected via Wifi or ethernet?