Well after many many hours, I am pleased to report success at last. I have learnt some lessons in the process which I am sharing here.
So, I had my repaired my Windows 7 installation as advised and I kicked off the Windows updates process manually. One hour or two passed and it remained stuck on "searching for Updates". My laptop became very sluggish and unresponsive. I identified that a process named "svchost.exe" was using more than 1 GBytes of memory. I killed the process and my machine started to respond again. But it also killed the update process with the error code mentioned in my earlier post. I did some more research and it has to be said that this site has a mine of very useful information. I noticed that NoelDP had mentioned on another thread to that updates can take a very long time on computers with what is nowadays a small configuration (2 GB RAM). I had also "reset" Windows Updates component by following a procedure found on Microsoft support site and for which there is a very handy batch script in a tutorial here.
I let mine run overnight and in the morning it had found 206 updates to installs. I let it run with all the updates and .... found that it failed after 3 hours and installing only few dozens. I followed the reset procedure again. And restarted manually the updates leaving it running overnight. It seems to take 5 hours to search and find some updates to intall again. I have read somewhere that there may be an issue when running the updates manually as opposed to letting the computer searching and installing updates automatically which my machine was configured to do at 3 am. I proceeded with installing the updates by batches this time, sorting them by categories. And after many days and night, eventually all updates seem to be properly installed. I also noticed that some individual .NET updates took hours to install so the only advise I can give is to be patient. Good luck to whoever is reading I am off to create a system image now because I don't want to have to go through this again. And thank you to members of this forum who provide a helping hand in dire time where it feels like throwing the machine away.

Windows Update KB3071756 Error Code 8007054f-wu_success.jpg