Yes you can!
first, you have to be able to download the application called Home Screen Wallpaper!
WARNING:
This isnt for the charging square, as it is only for the border of the apps.
:)
If it is an iPod Touch, yes, you can work on an iPod or use the iPod while it is charging.
The Ipod touch is done charging when the green battery on screen while it is plugged in if completely filled with green
because its not plugged in
yes you can
No, each iPod Touch comes with a charging/data transfer cable.
Your iPod will automatically turn on when you plug it in and start charging it.
buy a a new one
Yes, you can. Like most electronic devices, you can still use it when it is charging.
try charging it or connecting it to itune
mayby your battery ran out try charging it
It means it is charging.
When you get your iPod touch, it will include a pair of headphones, a quickstart guide, warranty details, a charging cable and two  stickers.