A. Really, we don't know. Windows 10 isn't out yet. It used to be that if you could receive Windows Updates (eg you were activated) than it would be able to upgrade to Windows 10, but they seem to have changed their approach since they originally announced that. Generally, if you get the "Get Windows 10" Notification icon, than your system can be upgraded.
I'd sort out the issue where it is showing as non-genuine, though. If Windows is still showing as activated (Right-click My PC->Properties) than it can be caused by malware, particularly given that it started after verifying system files- The "File Problem" you mention may very well have been itself caused by malware as well.
I can't tell if you actually have the replacement DVD they sent you originally, since you mention that they won't send another one (and of course you wouldn't request a second replacement if you still had the first replacement) If you do, though, that should be in the drive when you run sfc /scannow so it can replace the files it finds that are corrupted.