Linux Mint - changing settings is ineffective (even without reboot)

Question

After some update, the annoying and frustrating situation is the following.

• After each reboot the update icon shows the blue circle with '1' inside it; if I click on it, the update manager opens and shows the welcome screen
• I use custom font and colors in the terminal. After having set this options, if I open another instance of the terminal before closing the first one, it "inherits" the setting I chose, but if I close every instances and then open again, these settings are forgotten, so I have to set them again (font, size, colors, "don't show menu bar", ...).
• If I click on the desktop and press F5, the icons are disorderly put near the left edge of the main screen, like this: (I can reorder them by right-click > sort icons by name).
• If I right click on the desktop and then on desktop settings, I cannot change any desktop setting: not the Computer/Home/Trash/Volumes/Network icons' visibility, nor the "show icons on the main/secondary screen", not even can I change the wallpaper! Not even the theme, the color of the icons, and so on!
• In the right part of the menu bar I see removable unit icon, which, if hit, shows "file system radice" (radice is root) and "home", that you can also see in the preceding screenshot. (I cannot remove neither of them; maybe it's normal, but I never had this icon in the menu bar with no external drive connected.
• I cannot even change the setting of the menu bar (to make it hide automatically, for instance).

I think I could add a lot of other examples, but the main point is: no matter what setting do I change, nothing happens!

EDIT

Here's the output of the command, as suggested by @Bahamut.

...$ find $HOME -user root
/home/enrico/.android
/home/enrico/.android/adb_usb.ini
/home/enrico/.cache/dconf
find: "/home/enrico/.cache/dconf": Permesso negato
/home/enrico/AnthemScore/resources/license_utility

EDIT2

...$ env | grep -i session
XDG_SESSION_ID=c3
XDG_SESSION_COOKIE=2a5d5f96ef9147c0b35535562b32d0ff-1488028994.552913-205956845
SESSION_MANAGER=local/de-angelis-desktop:@/tmp/.ICE-unix/25348,unix/de-angelis-desktop:/tmp/.ICE-unix/25348
DESKTOP_SESSION=cinnamon
GDMSESSION=cinnamon
GNOME_DESKTOP_SESSION_ID=this-is-deprecated
XDG_SESSION_DESKTOP=cinnamon
DBUS_SESSION_BUS_ADDRESS=unix:abstract=/tmp/dbus-PA0bmxOIbi,guid=b51ee46103581d350dc85be758b18544
MDMSESSION=cinnamon

Answer 1

Not a clean solution, more a workaround. In the chat we found out, that Enlico build a Software from the sources, that install some libaries in /usr/local/lib.

ldd /usr/lib/x86_64-linux-gnu/gio/modules/libdconfsettings.so
1516

linux-vdso.so.1 => (0x00007fffa2c2d000)
libgio-2.0.so.0 => /usr/local/lib/libgio-2.0.so.0 (0x00007f1037207000)
libgobject-2.0.so.0 => /usr/local/lib/libgobject-2.0.so.0 (0x00007f1036fb6000)
libglib-2.0.so.0 => /usr/local/lib/libglib-2.0.so.0 (0x00007f1036ca5000)
libpthread.so.0 => /lib/x86_64-linux-gnu/libpthread.so.0 (0x00007f1036a5c000)
libc.so.6 => /lib/x86_64-linux-gnu/libc.so.6 (0x00007f1036693000)
libffi.so.6 => /usr/lib/x86_64-linux-gnu/libffi.so.6 (0x00007f103648a000)
libgmodule-2.0.so.0 => /usr/local/lib/libgmodule-2.0.so.0 (0x00007f10362870

snip

After rename a file in /etc/ld.so.conf.d/ that the installer created and change the

/etc/ld.so.conf.d/libc.conf 
# libc default configuration
# /usr/local/lib

this way and running sudo ldconfig The issue is fixed for the moment.