Ubuntu – adduser says user exists when the user does not exist

You become root with sudo su (as an example). Or better said: you elevate your admin user to admin priviliges permanently until you exit. Example:

rinzwind@discworld:~$ sudo su
[sudo] password for rinzwind: 
root@discworld:/home/rinzwind# 

And no Ubuntu technically does not have an active root user. From the Ubuntu RootSudo wiki page:

In Linux (and Unix in general), there is a SuperUser named Root. The Windows equivalent of Root is Administrators group. The SuperUser can do anything and everything, and thus doing daily work as the SuperUser can be dangerous. You could type a command incorrectly and destroy the system. Ideally, you run as a user that has only the privileges needed for the task at hand. In some cases, this is necessarily Root, but most of the time it is a regular user.

By default, the Root account password is locked in Ubuntu. This means that you cannot login as Root directly or use the su command to become the Root user. However, since the Root account physically exists it is still possible to run programs with root-level privileges. This is where sudo comes in - it allows authorized users (normally "Administrative" users; for further information please refer to AddUsersHowto) to run certain programs as Root without having to know the root password.

This means that in the terminal you should use sudo for commands that require root privileges; simply prepend sudo to all the commands you would normally run as Root. For more extensive usage examples, please see below. Similarly, when you run GUI programs that require root privileges (e.g. the network configuration applet), use graphical sudo and you will also be prompted for a password (more below). Just remember, when sudo asks for a password, it needs YOUR USER password, and not the Root account password.

To edit /etc/group directly use vigr

From man vigr

NAME
       vipw, vigr - edit the password, group, shadow-password or shadow-group file

SYNOPSIS
       vipw [options]

       vigr [options]

DESCRIPTION
       The vipw and vigr commands edits the files /etc/passwd and /etc/group, respectively. With the -s flag,
       they will edit the shadow versions of those files, /etc/shadow and /etc/gshadow, respectively. The
       programs will set the appropriate locks to prevent file corruption. When looking for an editor, the
       programs will first try the environment variable $VISUAL, then the environment variable $EDITOR, and
       finally the default editor, vi(1).

Hence, you can edit the /etc/group file with

sudo vigr

The format of group entries can be found in man. From man group:

NAME
       group - user group file

DESCRIPTION
       The  /etc/group file is a text file that defines the groups on the system.  There is one entry per line,
       with the following format:

           group_name:password:GID:user_list

       The fields are as follows:

       group_name  the name of the group.

       password    the (encrypted) group password.  If this field is empty, no password is needed.

       GID         the numeric group ID.

       user_list   a list of the usernames that are members of this group, separated by commas.

FILES
       /etc/group