Most optimal way of recovering files from a non-bootable MacBook in Recovery Mode
There's a fair bit to your question, but...

On one hand you tell us that you don't have an external hard drive or another Mac, but then you say you may be able to get your hands on an empty MacBook if you pay someone.

So, if you were going to be spending money, it'd be best spent on an external hard drive. Not only could you use it to get yourself out of this jam, but then you'd be able to use it as a Time Machine backup drive or even a temporary boot volume for your Mac.

Now to address your four 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?


No. You should have an external hard drive anyway, so while this is certainly one way to go to transfer your data, it still leaves you with no backup regime once you're back up and running. And, if you're thinking of doing this as a way to try and fix your existing drive, you may in fact hasten its untimely end. Basically, your priority should be to backup your data to another drive. Proceed on the assumption that your current drive will die very soon.


  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?


The method you use to transfer your data will not change the data itself. In other words, if your data is corrupted, then it's corrupted.


  3) More generally, what would be the better method of recovering my
  files that would optimize the amount of fully functioning files
  recovered?


Based on the info in your question, we can only assume your hard drive has started to fail. The first thing to do is not to overuse it at this point - as we have no idea how much life is left in it. In other words, you may only get one shot at this, if you're lucky. If you're really lucky, you will be able to recover all your data. Your hard drive may last one more minute, or it may last another week. We just don't know.

So, to maximise the amount of data you save, the absolute best option would be to buy an external hard drive and then to selectively backup your data in order of importance. The reason this maximises things is that you're selectively recovering what you want, whereas making a full backup will also backup an awful lot of stuff that isn't important. This is okay (in fact preferred) if you know the drive will last long enough to do this, but if you don't know how long the drive will last, then selectively backing up your data is a much better approach.

If you're not familiar with or comfortable using Terminal to selectively transfer your data, then getting access to another Mac is the best way to achieve this. Ideally you would have the other Mac and an external hard drive. That is, put your old Mac in Target Disk Mode and then connect it to another Mac to browse your data and copy it across to the external hard drive. But if you can't get both, then temporarily transferring your data to the other Mac is your best bet until you can also get an external hard drive to put your data on.

However, keep in mind that assuming your internal hard drive is dying, you will need to replace that as well, although with an external hard drive you could first install macOS on that and then transfer your data to it as well. This way you could use your old Mac for a while by booting up from the external drive. 


  4) In general, when such failures in installation occurs, what folders
  and files are likely to have been overwritten or erased?


This is impossible to answer as there is no way to know at what point of the installation process it failed. However, it's unlikely your user data would have been overwritten. Basically, unless you had formatted the hard drive, a macOS upgrade is only going to change system files, default apps, etc. It is not going to change your documents, media, downloads, etc.

A final word / recommendation

Having gone over both of your related questions I get the sense you need to perhaps make a choice between spending some money on getting access to another Mac or on buying an external drive.

If I was in your situation I would do as follows:


Purchase an external hard drive of higher capacity than your internal drive
Connect the external drive to your Mac
Boot up your Mac in macOS Recovery mode
Access Disk Utility and then format/erase your external hard drive
Proceed to install macOS onto your external drive
Once completed, your Mac should be booted into the new installation from your external drive. If not, restart your Mac and press the option key until you see your drives on the screen Then select the external drive and boot from that.
Once you're logged into your Mac, go to Apple > System Preferences > Startup Disk and make sure that the external drive is selected as the default Startup Disk
Exit System Preferences
You'll also notice in Finder that you can see the internal drive as if it's an external drive
Now you can do one of the following:


use Migration Assistant to migrate your data from the old drive
manually copy your data



NOTE: Once your data is copied across, you can use your Mac by continuing to boot from the external drive. However, this is not really a long-term solution as you'd be better to replace the internal drive on your Mac at some point or, when finances allow, upgrade to another Mac.