No, unfortunately that's not possible. you can download it to your ipod touch and you play the game but why would you get your apps on your computer when you have the app store on your ipod touch
Yes you can download apps to them from itunes on your computer (then transfer them) or straight to the ipod touch using a wifi connection.
with the ipod plugged to your computer open itunes and go to File/transfer purchases even if the apps you have are free
You can't play iPod games/apps on your computer. They have been specially designed for the iPod/Apple devices rather than on computers. If you have an Apple Mac computer or laptop then you can check the app store on your computer to check if there's a computer format of the particular game. This is rare though.
If you have downloaded new apps on your iPod which are not on your computer, connect your iPod to the computer with the cable supplied at purchase and allow it to sync.
Connect your iPod to your computer and sync it.
To download free apps from your computer to an iPod Touch, first install iTunes on your computer and sign in with your Apple ID. Open the App Store within iTunes, find the apps you want, and click "Get" to download them. Once the apps are downloaded, connect your iPod Touch to the computer via USB, select it in iTunes, and sync the apps to transfer them to your device. Make sure to keep your iPod Touch updated to ensure compatibility with the apps.
You can't get apps wirelessly without wifi but you can plug your device into computer.
When you sync the iPod, any apps you have bought on the iPod or another computer that are on the iPod will automatically upload to iTunes.
first plug in your ipod into your computer with the cable that came with it then click on your ipod and click on the apps tab at the top Then click the check box at the top and that should sync your apps on your computer to your ipod
If you do not open up iTunes and just plug it into the computer, it will only charge the iPod - no apps will be lost.
No there is not