maddogkm24 wrote:
I have a 2009 iMac that no longer supports updates. Can I purchase a new Mac Mini and use that as the new operating system for my 2009 iMac?
That question does not make sense. A Mac mini is a computer – not an operating system.
If by any chance, you are asking about Target Display Mode, that probably won't work. Although some 2009 iMacs (24" and 27" models – but not 21.5" ones) support Target Display Mode using Mini DisplayPort input, Apple added restrictions such that no recent or current Macs support using any iMac as a Target Display.
See the bad news here: Use your iMac as a display with target display mode - Apple Support