The real treat is to read your nice message and to be a member of such a fantastic group of people!
Following your advice to stick to a stable release I searched for info on how to install it and I found instructions in http://orgmode.org/org.html#Installation
telling me to run "M-x package-install RET org RET" from within emacs. I did it and it all looked like everything was running smoothly untill I was issued the messages:
WARNING: No org-loaddefs.el file could be found from where org.el is loaded. You need to run "make" or "make autoloads" from Org lisp directory
I am used to this since I first tried the cloned git version, but I noticed that there is no Makefile in the directory containing the newly dowloaded files (~/.emacs.d/elpa/org-20171113/), so I got stuck.
I haven't installed Org from within Emacs for quite some time now as I build it using make from its git clone. Also I haven't seen the warning that you see. Hopefully someone else can comment on that part.
I noticed though that the Org version you quoted: ~/.emacs.d/elpa/org-20171113/ is a bit old (not too old, but not the latest served on Elpa either). If you add the Org Elpa to package-archive as I suggested above, and install using the M-x package-list-packages interface, the archives will first get auto-refreshed, and then you can be rest assured that the installed packages are the latest versions.
I noticed that in the above installation instructions it is mentioned that:
Important: you need to do this in a session where no .org file has been visited, i.e., where no Org built-in function have been loaded. Otherwise autoload Org functions will mess up the installation.
so I repeated the process right after starting emacs with the --no-init-files option, then I added the line "(package-initialize)" to my initialization file but it still does not work,
What doesn't work? You shouldn't need to do --no-init-files. Simply make sure that your config is not doing (require 'org) directly or indirectly somewhere and you are not opening an Org file at emacs startup. That's all.
namely the old org-mode is loaded upon starting emacs.
How are you telling that? If you do M-: (featurep 'org) and it returns nil, it means that org is not yet loaded.
It is curious that I now have two org-mode entries in the top Emacs-Info node, one for the old version (7.9.3f) and another one for the new one (9.1.2 (release_9.1.2-37-g3f8d67)).
That's a different thing, has to do with the Info-directory-list variable, and is fine. You can have paths to Info manuals from multiple Org versions added to that var, and so you will see multiple Org manuals. I personally don't like that and so I surgically remove all the Org versions that I am not using in the current emacs session from load-path and Info-directory-list.
Could I have premanently messed up my emacs installation by not following the above Important advice?
Not trying to sound philosophical, but nothing is permanent. All the package installations happen in the elpa dir.. so to start the Org installation from scratch, you can rm -rf all the org installations from the elpa/ dir and restart emacs following that "Important" instruction and retry installing Org.