FileVault decryption process stuck + iCloud login fail + regular shutdown impossible. What is the problem?
I think you have received some bad advice from the repair shop, unfortunately.

It is correct that the 13" MacBook Pro 2012 model have issues with the internal hard drive cable. It hasn't got anything to do with overheating though. It is also incorrect that FileVault have anything at all to do with the cable problem.

The cable problems comes from the fact that the original cable was designed slightly too thin, while the inside of the casing is not completely smooth. Over time the friction between the two can cause the cable to fail.

You can replace the cable with another cable of the same type, which you indicate the repair shop did. The problem will just occur again. 

The permanent way to fix it is to replace the cable with a new type of cable that is slightly thicker. This is what Apple does if you take the computer to them. Another way to fix it is simply to add a piece of smooth tape to the case where the cable runs, so that friction is reduced.



You can find detailed instructions on how to apply the tape here:

https://beetstech.com/blog/prevent-a1278-mid-2012-hard-drive-cable-failure

You currently have issues with the file system on disk. This could be caused by problems with that cable - but it could also be the disk itself failing.

I would recommend fixing the cable issue as described above, and then restoring the known good backup you have. Make sure to do disk checks to make sure the disk is OK - if you get disk errors again, it's reasonable to assume the disk is broken and needs replacement.