I'm helping a friend to upgrade his iPad 2 GSM to iOS 5.1.1. We downloaded a version online
But for some strange reason iTune cannot upgrade the iPad to this version.
Where can we download the proper iOS 5.1.1 for his iPad?
Older versions of th software are no longer supported. Even if you can find them, iTunes won't verify them. Sorry.
You can't update to iOS 5.1.1 on an iPad 2, iOS 6.0.1 is the only version that is 'signed' by Apple for it.
For YouTube there are alternatives e.g. google have an iPhone optimised app and they are apparently working on an iPad version, and there is Jasmine, and your friend could try accessing the mobile version via Safari : http://m.youtube.com
For maps, Nokia are reportedly working on a maps app (and there is their website) and there is google maps via Safari (http://maps.google.com).
Not sure what you mean by 'maintaining'. You can only use iTunes to sync music, films, tv shows to the iPad's Music and Videos apps. Other apps may allow you to copy content to/from them via your wifi network, and some also support Dropbox and email. You can also backup to the cloud.
This is my theory ....
Apple doesn't support downgrading the software and Apple may not be signing the "upgrade" that you are trying to apply, so matter what you try, it may not work unless you update all the way to iOS 6.0.1. The iPad is being recognized by its serial number and therefore a non supported upgrade may not work.
iOS 5: Updating your device to iOS 5 or Later
How to install iOS 6
iOS: How to update your iPhone, iPad, or iPod touch
If you are currently running an iOS lower than 5.0, connect the iPad to the computer, open iTunes. Then select the iPad under the Devices heading on the left, click on the Summary tab and then click on Check for Update.
Tip - If connected to your computer, you may need to disable your firewall and anitvirus software temporarily. Then download and install the iOS update. Be sure and backup your iPad before the iOS update. After you update to iOS 6.x, the next update can be installed via wifi (i.e., not connected to your computer).