Fix a sometimes happening prohibitory sign
When you get a prohibitory sign when you attempt to boot, it means your Mac can't find any bootable media.

This is the EFI firmware searching for a device to boot from and not having any success.  It has nothing to do with the file system, so First Aid or even reinstalling will not fix the problem.

The most likely cause of this problem is a failing drive.  You have to get a new one.


  I have an old backup that's lacking some files. So I guess, if I
  backup now it's going to backup the whole drive including system
  folders errors.


That's no reason to not attempt a backup.  Your objective right now should be to backup your data and if it causes an error, so be it.  Losing a few files is far less damaging than losing all of your files.