The process you describe as "Saving iPad to iTunes" is called backing up the iPad to iTunes.
And if you are on iOS 5.x you can use iCloud as well.
Basically when you connect your device to iTunes, you can choose if you want to sync wireless (which is recommended but might be painful as sometimes it doesn't work as fine as Apple wants people to believe) or tethered (via the USB cable).
Either way, the premise is that every time you try to sync the iPad to iTunes (either tethered or WiFi) it will make a backup (I think it only does it once per day, the backup part).
You can also force a backup by right clicking your device on the left panel on iTunes.
After you have the backup, you can reinstall the firmware (fresh) and then restore from that backup.
And will it just save the game apps, or will it save the app and the level you have reached on it? Thanks for your help.
It will save all of your settings and app's data (for ALL apps).
So I guess if you are trying to say "Will it save the level I was in, on a given game" the answer is "Yes". Same for a note taking app with your notes and so on...
With iCloud backup (enabled on the settings app on the iPad) it's the same, only that if you have too much data, iCloud has a 5 GB limit and after that you need to pay.
And your app per se (the installer) will never be saved on an iTunes backup (iTunes holds the installer for that app on its library so...), and the same happens with an iCloud backup (iCloud can communicate with the AppStore directly so why would it save 10000000 copies of the same app if it just can save the link to it).
