psql fatal role does not exist

Use the postgres user:

sudo su postgres

and then use psql.

If you still face problems check this link: PostgreSQL error: Fatal: role "username" does not exist

sudo -u postgres createuser user

may help you to create a new user with all the privileges of postgres

As pointed out in the comments, your pg_hba.conf seems fine.

Usually, the database will run as the postgres user (check ps aux | grep postgres to find out the username postgres is running under).

Log in as that user, for example sudo su - postgres, then create a user matching your normal Ubuntu user account (createuser username), and finally create a database with that same name and set the owner (-O) to that database user, like this: createdb -O username username).

That should make calling psql work, and pgadmin - as long as you start it as your default user, username - should work as well.

Edit: By default, psql will use your Linux username as default value for both the database-username and the database-name. You can override the username by using -U someotherusername, and connect to a different database by adding that DB name to the command line, such as psql someotherdbname. You might also find psql -l useful for listing the existing databases.