no you cannot use ipod and iphone apps on itunes, but you can buy the apps on itunes and put them on your ipod and iphone
Sync your iPhone to iTunes on our computer
If the applications are downloaded via iTunes, they will be automatically transfered to the iPhone during synchronization. Otherwise, the apps downloaded via iPhone will be copied and backed up to the iTunes during synchronization. So to transfer the apps to the iPhone, just connect the phone to the iTunes and sync. Click on iphone on the side bar, then apps up the top, then sync apps.
itunes will back up your apps when you sync your iPhone if the computer is authorized (store-authorize computer in itunes).
Connect your iPhone/Pod to your computer/laptop, open iTunes and sync your iPhone/Pod. The apps will then appear in your "applications" tab of iTunes.
As long as your computer has itunes that is authorised on the same itunes account as your iphone, then it will automatically transfer all your iphone apps onto the computer
By the time I answer this question there are ~285,000 iPhone / iPod Touch apps on the iTunes App Store.
You would need to browse the internet to find apps that work with the iPhone tat you do not need to download via the iTunes store.
you cannot play iPhone apps on your computer. And if you want to open games from your iTunes then you cannot either. iTunes is only for songs or games, videos, photos and apps for iPhone.
You would need to have an iTunes account.
You can go to apple.com and download iTunes
With over 50,000 apps available on itunes, it's hard to choose a favourite, I have almost 100 on my iPhone.