Let me first mention that a related question and answer is given in Backup to External in Recovery Mode (Terminal or Time Machine) . For the sake of completeness, I will tell the complete story about my recent nightmare.
Some days ago, I was trying to update my MacBook Pro (13 inch version from 2011) from Sierra (the latest version of it) to High Sierra. However the installation failed and I received a message that I should restart my computer. By clicking the (unique) option "Restart", I ended up with a prohibitory sign after some time.
I tried to use First Aid on Macintosh HD from Recovery Mode. It failed miserably and the details contained a bunch of "Missing thread record" followed by some numbers. The final message after the failed process was the following "First Aid process has failed. If possible backup the data on this volume. Click Done to continue".
I tried to access the Internet Recovery Mode following the advice of the Apple support. It failed giving the error -2002F.
My third attempt was to use the Single User Mode in order to apply the fsck command. However I could not even start to write in the terminal since it was going crazy in a loop by giving the message that the Root could not be found (the number of the error if relevant was probably 19). After some time, everything stopped and the background got white, while the letters got black.
As I understand, now my only option is to backup through Recovery Mode following the options mentioned in the above cited question and, then, erase my Hard Drive through Disk Utility. If I have any other available options, please, let me know.
The problem is that I don't have an external hard drive and also I don't have another MacBook. I will try soon to borrow an external hard drive from a friend.
Now, I shall ask my questions.
1) Suppose that I can have access to another MacBook. By using First Aid through another MacBook in my Hard Drive in the Target Disk Mode, would I obtain a better result? In other words, does the First Aid of Disk Utility acts differently when applied through another MacBook than when applied through my Recovery partition (assuming that my Recovery partition is fully functional)?
2) Suppose that I transfer my files to an external HD through any of the methods in the above cited question and, when trying to access the transferred files, discover that they are actually corrupted. Would they also be corrupted if I have instead performed the transference by using another MacBook and the Target Disk Mode?
3) More generally, what would be the better method of recovering my files that would optimize the amount of fully functioning files recovered?
4) In general, when such failures in installation occurs, what folders and files are likely to have been overwritten or erased? More precisely, what folders are modified by updating from Sierra to High Sierra when the installation completion is successfully achieved?
I ask these question because I may be able to get my hands in an empty MacBook if I pay someone, therefore I would like to know beforehand if such action would indeed be optimal.
Thanks in advance.