I can't find apps that I've just downloaded out of I tunes on my Mac mini

Downloaded from where?

The Mac App Store?

Did you look in yur dowloads folder?

If from Mac App Store, go to the purchased tab in the Mac App Store and see what it says by the app.

Have you looked in the Applications folder, the dock or Launchpad?

When you say you downloaded apps "out of iTunes" that would imply iOS apps for the iPhone or iPad. Those will be found in ~/Music/ITunes/Mobile Applications where ~/ indicates your home folder. You can install them on the iDevice by attaching it to your computer with a USB cable and launching iTunes.

I you meant you downloaded them from the App Store, those are only for OS X and will be automatically installed in the /Applications folder on the hard drive root.