My WD external drive unmounted itself and now does not work
Either your WD MyBook enclosure has failed or the disk itself has failed.

I am basing this assessment on two factors:


Points 4 &amp; 5 above - that plugging it into different computers didn't work.  If it doesn't work on different computers you have narrowed it down the the WD unit itself.  If the problem was with your Mac, it wouldn't be present on a different computer.
The correct response  provided by diskutil for disk1.  It's highly unlikely (though not impossible), that if the enclosure wasn't functioning you would at least get erroneous information back or no information at all.  The WD enclosure is reporting back that there is a drive but it has no operating system.  Chances are, it's the drive.


However, you can take it a step further and do some additional diagnostics.  The key here is to isolate the major individual components of the WD enclosure - the logic board and the drive itself.  

So, to diagnose this you will need either of the following


a known working hard drive 
a 3.5" HDD to USB adapter (I recommend this option for reasons that will become clear momentarily).


You will need to disassemble the MyBook.  From my research, the case appears to be held in place with "snaps" which you just pry off so it shouldn't be too difficult to get into.  There's a straightforward set of instructions on Instructables.com

Depending on the option you took above - you either need to change the drive in the MyBook  or plug the old drive into the USB to SATA adapter.

If one component works (i.e the drive), then you know for a fact that the other (i.e. the enclosure) has failed; or vice versa.

If it is your drive, the USB to SATA adapter will allow you to attempt to recover your files.  I have personally used Disk Drill with excellent results (it's free to use the diagnostic portion and to see if you can recover data).  You will be able to make an image of the drive and attempt recovery on the image lessening the chance of total failure of the drive.

If it happens to be the enclosure, the USB to SATA adapter will allow you to continue to use the disk drive while you come up with a more permanent solution (the MyBook is essentially the same thing but with a more elegant enclosure).

If you choose the "drive method" you will still be able to get the same diagnostic results, except you won't be able to transfer or rescue any data if it happens to be the MyBook enclosure that's bad.

Now, as preventing it from happening again - well, this is a spinning hard drive which means it mechanical.  It's going to fail.  The only thing you can do is mitigate data loss by having a backup