top posting here, just to say a big thank you to all who answered, Samuel (the first one so this reply is to his mail message..), Roberto, sixpack13, Dave, Chris (and Cameron while I'm writing...)
Ah, guys; this remembers me the old days when I approached for the first time Linux and while trying to install Slackware 3.0 from Yggdrasil on an HP workstation with Matrox card I posted on linux kernel mailing list to ask help to run X Window System environment and in a few hours Alan Cox in person answered giving two possible solutions (one of which to recompile kernel...) that both worked, wow!
Six cd set with Slackware 3.0 still here like a relic... ;-)
https://drive.google.com/file/d/1XCuyJX3-hch4K_U97WhxaBYNChhWm5-D/view?usp=sharing

So some help/confirmations still needed, see below

On Fri, May 10, 2019 at 6:57 PM Samuel Sieb <samuel@sieb.net> wrote:
On 5/10/19 4:37 AM, Gianluca Cecchi wrote:
> One further info is that the disk is seen marked as gpt from fdisk.

Yes, that is required for UEFI.

> Having searched around in the mean time I found some further info, as I
> have not been quite familiar with gpt disks until now...
> It seems gparted doesn't work well with gpt and many advise to use
> gdisk/sgdisk utilities instead, if I have understood correctly

You must be seeing really old info, because I've been using it for years
with no problem.


Probably I had to specify also that in Windows 10 the partition I have to shrink appears as bitlocker encrypted and in some places I found that in this case the only option is to shrink from within Windows. But it could be old info too..

Anyway I was able to shrink the partitions and so I have now an allocated space in the middle.
 
That's correct.  (I assume you mean the 475GB partition though.)
Usually you will also want a /home partition as well.

Yes, the "7" key (and others) works no more in a good way in my 7,5 years' old Asus U36SD and this is one of the reasons I bought a new beast...
Original 475 became 45... ;-)
 

> I have doubt about numbering, because p3 will become smaller and if I
> create in the middle of p3 and p4 two more partitions, what will happen?
> And could I still use the Windows Recovery one...?

Yes, it's all fine.

Ok. Also noticed the info in another answer regarding Windows Media creation tool... and partition numbers independent from their physical position in gpt
thanks
 

You can try, but I find it doesn't work as well as gparted.  Just make
sure you backup anything important from the Windows side. 

I made a dd of the entire disk from a live distro (Slax) via network (but this is another funny story when nothing works as expected when you need it, hello Murphy)

So far so good I created a live usb key from F30 workstation x86_64 UEFI version and I was able to start it and begin the installation.
I chose "custom" option in Anaconda for partitioninh and this is the layout seen:
https://drive.google.com/file/d/1iP7AjSmqeSSIN-NbK9NXrmX_38UFhrzX/view?usp=sharing

I have a doubt because the current EFI System Partition is in the below part under the "Unknown" group, while in several links (regarding older Fedora versions) it was in the upper part too as if it had been "recognized" by the installer to be managed by grub in the latest stage....
see eg here:
http://linuxbsdos.com/2016/12/01/dual-boot-fedora-25-windows-10-on-a-computer-with-uefi-firmware/

where the sda2 partition appears both in the upper side with grayed label "SYSTEM" and in the Unknown group too....

Can you confirm it is safe to proceed and create the partitions for Fedora?
Despite suggestions I plan to create only the partition for "/" and a swap partition
I don't need very much the /home one. And often I put docs and such inside the ntfs-3g mounted Windows partition so I can access them both from Linux and Windows (even if I have t pay performance/cpu cycles penalty for this).
I rarely boot Windows (7) on my current laptop, but for example I had to do just two days ago because I had to connect it to a usb-donkey based projector and no driver for Linux... argh and to have access to the files was a big plus

Cheers,
Gianluca