Ubuntu – Is it possible to unset root password

ssh root@localhost uses the same password for root. It looks like you have not set root password. To do that log in as root using sudo -s then use passwd command to set root password.

After that you must be able to ssh as root

• How to find out root password for installing software

What is meant by an unset password? Is it blank? Is it null? Or something else more cryptic?

Is just inexistent. Root account is disabled by default, hence it doesn't need password. So, what most resemblance has is undefined (in JavaScript) or (null) (other languages). It is just unset.

How does the account becomes enabled once I set password for it?

Actually, setting the password is just part of it, but doesn't enable the account. You need to enable the account using:

sudo usermod -U root

and then set the password with passwd.

what does an ! in password field mean?

Extracted from man shadow:

A password field which starts with a exclamation mark means that the password is locked. The remaining characters on the line represent the password field before the password was locked.

It could mean that the account is locked. But also:

If the password field contains some string that is not a valid result of crypt(3), for instance ! or *, the user will not be able to use a unix password to log in (but the user may log in the system by other means).

Either way, any account with ! can't log in with applications that use the shadow file.

How come this encrypted form is only one character long?

Is not encrypted. See above.

And does an account become disabled if I put an ! in the (encrypted) password field?

See above too.