Mac mini Server Password Locked

I think you would need to make them actual users, and then give them screen sharing access to the system.

Or, you could give them SSH access and write some kind of shell script (perhaps embedded in an Automator/AppleScript application) that changes the password using unix tools.

Or, you could enable Apache server and write a PHP application that changes the password from a webpage. This is what I would do but it's only a good idea if you're capable of doing this in a secure fashion.

The 'Guest' user does not have a password.

The command you are using: dscacheutil -q user -a name guest always outputs 8 stars (********) no matter what password the user actually has set. As OS X only stores the hashed password, there is no easy way (besides using a password cracker) to recover passwords.

Edit: Hashed, not encrypted.