How to enable "Repair disk button"?
You are getting the read-only file system error because on OS X NTFS is natively read-only. It was read-only before your Time Machine run in, and will stay that way unless you install a third-party driver, such as Tuxera NTFS.

Disk Utility's built-in repair commands are merely a GUI front-end for fsck and fsck_hfs. They are not meant to be used on an NTFS-formatted disk.