So you can handle #1 a number of different ways, but I'd generally advise against using MC as your "shell", although you can definitely start the xserver with only JRiver and no window manager (just edit your .xinitrc to launch MC instead of a window manager and then "startx"). The problem with that approach is that if jriver crashes it will dump you back to the terminal. You need some kind of minimal window manager behind the scenes. The good news is that linux has lots of choices for extremely minimal window managers that don't actually have to occupy any screen real estate (like openbox or i3). So with those kind of minimal window managers (properly configured), you can have MC running full screen and no real likelihood that anyone will be able to launch anything else, but you'll have an easier time recovering in the event that MC crashes (you can use a systemd service to automatically relaunch jriver, etc.).
In my experience with Debian (rather than Ubuntu), it's fairly easy to install just the minimal pieces you need rather than a full "desktop environment package" (just don't select a desktop environment during the install, and then install the pieces you need later). Another advantage of Debian is that you're also using an officially supported platform for MC if anything is acting funny. My "kiosks" around the house use debian, lightdm with autologin configured, and a fairly minimal openbox environment with no panels so it just looks like jriver is running with nothing "behind it."