Just an idea. Copy all the data you can from that external drive to something else just in case that’s all you can get. Plug the external drive into the Mac with the bad drive. Connect the Mac to your network with a Ethernet cable, turn on the Mac while doing command option r combo when you see the Apple. Go to disk utility and format the external to hfs (it will wipe the disk). Exit disk utility and go to the install mac menu. once install on the external drive is complete restart while holding down the alt key and select the external. Boot off the external drive. Recover data by copying it to the external boot drive or another external you have. You may want to test the command option r first and I would disconnect the failing HDD during most of that process.
Hmm, one less pedophile and one less Russian. Give the Brit a medal.