Have iOS apps. Can I use them on my Mac Mini? I bought many iOS Apps on various iPads and iPod touchs. This Wednesday I will have my first Mac, a Mac Mini, so my question is: Will I be able to download these Apps without any charge, if they are available on Mac Store?

I ask this because I have been watching some videos and have seen GarageBand on the Mac but I don't know if it's the same App. I know that the App Store and Mac Store are different, but, like some Apps on AppStore have a plus symbol on their icons corners saying these Apps can be run on iPad, iPod touch and iPhone I wonder whether there will be some Apps for both iOS and the Mac.

Also, I don't know if GarageBand was released on Mac before iOS devices.
At the moment, you can't really do this. Although I suspect that Apple is looking to integrate iOS and macOS in the future so that this sort of thing can be done (purely speculation).

GarageBand on the Mac is different from the iPad version (it's more comprehensive) and it has been available on macOS for far longer than on iOS.

It is possible to run iOS apps in the Simulator app that comes with Xcode. However, it's not as simple as downloading an app from the App Store. You'd have to get the source code for the app, compile it in Xcode and run in the Simulator. Most apps being closed source, this won’t be possible!