Thanks to everyone for the invaluable support.
Through your suggestions and a lot of trial and error, the system now works as I expected.
Issues 3, 4, 5 and 6 have been solved setting LAN on both computers to "Private".
Issue 7 was harder to solve, and, to be sincere, I am not able to say exactly which settings led to the desired result.
Last obstacle was that I could access Desktop via its LAN IP and not via its NAME (i.e. via \\ipaddress and not via \\desktopname).
This morning also this obstacle has disappeared: clicking the Desktop's icon in "Network" now gives me access to every shared folder and disk in Desktop.
Again thanks!