You can use Disk Utility to create an image of the external hard drive.
Plug in the external hard drive and then start Disk Utility--it's in the Utilities folder under Applications--and then select the external hard drive from the list along the lefthand side of the Disk Utility window. Once you've selected the external drive, click on New Image at the top of the window and it will ask you where you want to store the image file. Select a location and then let it do its thing.
Once completed, you can restore the image to the same or another external drive or you can simply double-click the image file to mount the disk and explore its contents using finder as you would normally.
There is absolutely no way that you should even think about doing any of this without a complete backup on a separate disk. Verify the backup before beginning.
1) If you have a complete backup, the easiest way to do this would be to wipe everything, make the partitions you want, and then copy the information back from your backup. If your Recovery HD is deleted, there is no way to re-create it without reinstalling the OS. (At least none that I could find when I was searching recently.)
2) Assuming you have a backup OTHER than that Backup partition, if you want to attempt to merge these, I would try it in this order:
a. Delete the 'Backup' partition.
b. Merge 'Data' partition and former 'Backup' partition.
c. Merge System partition and other partition.
d. Re-create the 'Backup' partition and restore it from whatever backup you have.
I have done several live-system partition resizings with no problems. However, the one time that there was a problem, I had to reformat the entire drive and start over.
Best Answer
macOS's mv is based on the BSD source code. You can find the source code to the mv command online. Using https://github.com/freebsd/freebsd/blob/master/bin/mv/mv.c as a reference, you can see that they do indeed first try to rename the file and then if it is crossing filesystems, it does a cp followed by a rm.