Can Linux OS be installed on Mac Mini; 2.8 GHz Intel Core i5; 8 GB 1600 MHz DDR3; Intel Iris 1536 MB?

Depends on whether you mean to replace OSX, dual boot with OSX or, run it in a virtual environment.

Linux OS is not an OS btw, It's a generic name for all versions of Linux.

Yes, See:

Easy clean install of Linux on MAC Mini (or other MAC computers)

Using the free VirtualBox 5.0.16 virtual machine, I have Ubuntu 15.10 (with Cinnamon Desktop Environment), and Solaris 11.3 running with El Capitan 10.11.4. Click to enlarge.