If you are making reference to your suggestion of 23th Sept (restart as new), I'm sorry but I can' t consider that a solution, but more a "resignation".
In fact, immediatelly after the incident I did two things:
1. Perform a backup and restore. The problem remained (yes, I know it was a long shot, but I had to try)
2. Restart the iPhone as new and check that I could install any app : everything worked fine.
Next thing, I restored again the backup, with the foreseeable result: apps don't work and can't be installed throug App Store. And that's the present state of my iPhone.
Stupid? Well, the reason behind is that there are 21k photos in my iPhone, coming from a variety of sources: all the iPhones and reflex cameras I've owned for the past 10 years or so (I've done random checks and all of them seem to be well). I had iCloud Photo Library activated (besides this, I several backups in offline disks, with the original sources, but unfortunately dispersed and possibly lacking some photos). No problem then...or so I thought.
The problem awaiting was that iPhotos.com reported that there were some 17k photos in iCloud. Where have the remaining 4k gone? At first, it seemed that the sync between device and cloud hadn't finished, as the Photos app reported 'uploading xxx items'. So I let it fininish. With a lot of patience, as the upload speed is around 1k photos...per day (with 2 or 3 occasional bursts of high activity). To make a long story short, the uploading process has fininished today.
The end result? iCloud.com keeps reporting 17k photos.
I've started extracting the photos directly from the iPhone, using an utility called iTools.
We shall see.
Thank you any way for trying to help.
(PS: I haven't mentioned my hours talking to Apple support people about this. Their final recommendation: restart as new)