Ubuntu – user does not exist in /etc/passwd when trying to change the default shell

You're doing it wrong (tm) :)

In your terminal window, look at the "command prompt":

username@hostname:~$

What is username there? You can also try entering whoami[Enter] to see your current username.

From you description it looks like you entered something like

sudo su www-data

or somehow else opened a console session as www-data user. This user has no rights to use sudo command, so your attempts at using sudo fail.

www-data user also has no password set by default, so it is impossible to log in directly as this user. Which is good. You do not want to give it a password.

You need to open another session as your user (or exit your current www-data session) and type the commands there:

sudo chown yourusername:www-data /path/to/directory

which will ask you for your login password.

(or, maybe, just move your stuff to /var/www which already has correct permissions. Then you can add your user to www-data group to get read-write privileges to that directory)

PAM has a pretty tight hold on chsh. As you can see form /etc/pam.d/chsh, it's doing a check:

# This will not allow a user to change their shell unless
# their current one is listed in /etc/shells. This keeps
# accounts with special shells from changing them.
auth       required   pam_shells.so

There's also a man page for this check (man pam_shells) which tells us the following:

pam_shells is a PAM module that only allows access to the  system if the users shell is 
listed in /etc/shells.

It also checks if /etc/shells is a plain file and not world writable.

So by the sounds of it, you don't have a /usr/bin/zsh line in /etc/shells. Let's add one:

echo $(which zsh) | sudo tee -a /etc/shells
chsh -s $(which zsh)

Either that or your current shell isn't listed on there. If you're stuck on something like rbash, that might not be a listed example and that might stop you from changing shell.

I tested (removed the zsh line from /etc/shells, loaded zsh and tried to chsh) but saw a very different error message:

You may not change the shell for 'oli'

So it's probably not this.