Ipod touch battery question?

i just got an ipod touch for my birthday...i have 2 questions as i'm willingly dragged into the 21st century :-)
does it charge while hooked up to my computer with the usb cord?
and how can i tell if it's still charging or fulling charged?

thanks in advance for any help you can give!!!
Update: it didn't come with an adaptor, don't know if this matters but it's a 2nd generation...and how can i tell if it's charging or not?
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