How can I find the serial number of my Mac mini? Do Mac mini come with a unique serial number? How do I find it?

It is a model without optical drive.
Yes. They come with unique serial number. You can find the serial number as per Apple Support Document.

Mac mini: How to find the serial number

In Mac OS X

On most computers with Mac OS X, you can find the serial number in the About This Mac window.



On the surface of the computer

On Mac mini (Mid 2010 and later) computers, the serial number is printed on the metal frame without a bar code: