Is Mac Mini enough to publish my game on iTunes or do I need iPod or iPhone to publish the game on iTunes? I have a simple trivia game where you basically click on one of the 4 buttons the whole time, nothing else, maybe except the main game menu.

My question is, if I need to own anything else except my Mac Mini to publish this game on iTunes or I need some mobile device like, iPod Touch 4 etc.

If it's not possible to go without iPhone/iPod (iPod Touch with iOS 4.1), which device is then the minimum? As I said, it's a simple game, no motion graphics, few simple effects after the answer etc.

My primary phone device is Samsung Galaxy and this would be my first iOS port of my trivia game for Android, so I am not sure if Mac Mini is enough or I need for this type of game/quiz something better?
As a user I would hope that you have run the app on the IOS device that Iuse. Thus iff you say it runs on an iPad you have run it on an iPad, if I have an IPhone you have run it on an iPhone etc.

If I have a problem I expect you to be able to reproduce it on the hardware I have or be able to say that you see no problem on the hardware.

No simulator is perfect there will be differences between it and real running - especially as they use different types of processor etc. One example of this as pointed out by 0x7fffffff is that the file system in the simulator is case insensitive but on a IOS device it is case sensitive

So I would expect professional support to have run the app on at least an iPad and an iPhone and preferably on various models e.g. iPad and iPad mini, iPhone 4s and 5.