At least a part of the question - how to get rid of the message about the need to install libc6: i386 - has a solution that the steeldriver brought me to.
He led me at the ESET support page. I see that my 'Recommended updates (xenial-updates)' are checked, similarly as 'Recommended updates(trusty-updates)' for another Linux distribution in that manual and I hope the alerts
me@furtherPC:~$ software-properties-gtk
/usr/lib/python3/dist-packages/softwareproperties/gtk/SoftwarePropertiesGtk.py:40: PyGIWarning: Gdk was imported without specifying a version first. Use gi.require_version('Gdk', '3.0') before import to ensure that the right version gets loaded.
from gi.repository import GObject, Gdk, Gtk, Gio, GLib
/usr/lib/python3/dist-packages/softwareproperties/gtk/SoftwarePropertiesGtk.py:40: PyGIWarning: Gtk was imported without specifying a version first. Use gi.require_version('Gtk', '3.0') before import to ensure that the right version gets loaded.
from gi.repository import GObject, Gdk, Gtk, Gio, GLib
me@furtherPC:~$
don't matter. Software Updater tells that my Ubuntu 16.04 is up to date.
The recommended commands
sudo apt-get update
sudo apt-get upgrade
worked without warning. After the furtherPC restart
as_a_root@furtherPC:/home/me$ sudo dpkg --add-architecture i386 && apt-get install libc6-i386
[sudo] password for as_a_root:
E: Unable to acquire the dpkg frontend lock (/var/lib/dpkg/lock-frontend), are you root?
as_a_root@furtherPC:/home/me$
has not worked but
as_a_root@furtherPC:/home/me$ sudo apt-get install libc6-i386
has downloaded and installed 10.4 MB files. Now running that installation file
as_a_root@furtherPC:/home/me/pathESET$ ./eset_nod32av_64bit_cs.linux
No protocol specified
(eset_nod32av_64bit_cs.linux:5531): Gtk-WARNING **: cannot open display: :0
as_a_root@furtherPC:/home/me/pathESET$
will not raise the message that libc6: i386 is needed, however it reports further errors. Perhaps I understand correctly that
me@furtherPC:~/pathESET$ dpkg-query -W libgtk-3-bin
libgtk-3-bin 3.18.9-1ubuntu3.3
me@furtherPC:~/pathESET$
means that the furtherPC has the required GTK + 2.6 or newer installed. I have also asked ESET support and will tell the result here.