Update 1: Somehow, after unconnecting and re-connecting, the original disk (disk1) has now returned to original state, with the readme file as well! I still have another disk which is not working. When connected to my MBP I get the message, "The disk you inserted was not readable by this computer." "[Initialize | Ignore | Eject]".
Update 2: @Allan's question: Like how long from when you bought the drives and were working to when they stopped? Answer: They were removed from the packaging on the day they arrived. These are brand new. They both worked out of the box. Issues started after attempting to partition and attempting to restore via Image.
Update 3: The disk currently does not work on Mac or Windows. Next steps from here?
TL;DR:
I ordered two external hard disks and tried them on the first day they arrived. They appeared to work as a normal external hard drive when I first connected them to my MBP (Retina mid-2015, Yosemite 10.10.3). However, after trying to partition/restore via Disk Utility, they become both unusable. NB. One of them returned to original state — please see Update 1, 2 and 3 above. So please also see my attempts at a solution in my answer to this question as advised by @bmike
If these types of 2.5" external hard disks are actually not compatible with Macs or Time-Machine backups:
A) What can I do to return the disk back to its original usable/exfat state?
B) In their original Exfat state, to what extent will they be usable?
C) Why are they limited to Exfat format?
D) How, without the seller telling me, can I know these are limited to Exfat format only? e.g. Are certain cheap 2.5" external HDDs from China always limited to Exfat?
Quick Intro: I first tried to partition one of them. This made it unusable. After attempting to restore the first one by copying/cloning an image from the second one, the second became unusable. Then somehow the first disk randomly became usable again and was back to its original state (it even contained the original readme file).
Context:
I want to do a Time Machine backup to an external hard disk so I bought two 2.5” 2TB external hard disks.
The hard disks (both identical) were described as compatible with macOS, both on packaging and on the online description. I connected one of them for the first time and all looked normal. The only exception is that I found a readme file, which mentioned this drive can only be formatted to Exfat.
So my conclusion is that the drive is officially in NTFS format, while the readme file says it's Exfat only and the online description and packaging say's it's compatible with Macs. I contacted the seller, who replying saying that it doesn’t work with PS4 and is compatible with Windows, Mac, Xbox and Linux.
So after attempting to partition 1.1GB for Time Machine, Disk Utility gave me the message “Unable to write to last block of device”. In an attempt to salvage the first disk, I wanted to basically copy/clone the second external drive in its original format and burn it onto the first one that no longer shows a volume. I plugged in the second disk and tried to use the ‘Restore’ function via the Restore tab and clicked on the ‘Image…’ button. I then got a message saying:
"Unable to create “JMicron Generic Media1.dmg.” (Input/output error)."
The first screen shot is what the hard drive first looked like when connected to my MBP. The second shows what it's like after it became unusable. Below that are screen shots in chronological order, whilst attempting @Allan's suggestion.