Q: How do I upgrade iPod touch to ios 6.0

   If it's one of the first like you say what generation? It most likely doesn't support (iOS6) so your out of luck with that website since they changed they're credentials.

It must not be a 4th generation. If it's too old it can't get it. Sorry about that

As Zach stated, a 4th generation iPod or later is required for iOS 6. You say your model does not have a camera, so it is a 3rd generation or earlier and cannot run iOS 6. If you are running iOS 2 as you stated in your product list, you probably have a 1st or 2nd generation iPod. If it's a 2nd generation, update to iOS 4.2.1, and the App Store should offer to download an older version of the Facebook app.

Not sure which generation you have? Model Identifier Utility

If the iPod does not have volume buttons on the upper left edge it is a 1G iPod. Those can only go as high as 3.1`.3 that you get here:

Purchasing iOS 3.1 Software Update for iPod touch (1st generation)       

https://buy.itunes.apple.com/WebObjects/MZFinance.woa/wa/touchLegacyLandingPage