Time Machine Fails

I am running MacOS 10.13.2 and have finally decided to start using Time Machine for backups. However, I cannot seem to complete the first backup! The backup starts and runs for a while and then I get the message "Backup Failed - Time Machine couldn't back up to <name of my disk>".

I have a Macbook Pro (Retina, 13-inch, Early 2015) and a USB-connected WD My Passport Ultra 1TB as backup drive.

After each attempted (and failed) backup it is no longer possible to unmount the disk. If I try it says that some "The disk <disk name> wasn't ejected because one or more programs may be using it."

I have tried a lot of different things:

- I have rebuilt the Spotlight index, tried turn it off and on globally and on the disk.

- I have erased the disk, tried First Aid (in disk utitility) for both the external and the internal drives. I have done these things at multiple times.

- I have also tried force ejecting the disk after a failed backup. Then connected it again and tried again (without deleting the failed backup file .inProgress). After a few attempts I have usually managed to get the backup running again, but only for a while. The closest I came with this methods were a few gigabytes away from finish, but at that point the amount that is left to backup is just counting up at the same time as the backed up amount. For e.g. it can say Backing up 2.4 GB of 5.0 GB at one time and a little bit later Backing up 2.8 GB of 5.4 GB etc.

I am at a loss! Also, I believe that the failure to unmount the disk after a failed backup has something to do with spotlight. If I try to delete the failed backup file from the disk I get the message: "The operation can't be completed because the item ".spotlight_repair" is in use."

Any help on this issue would be greatly appreciated!