When using a mains charger, as well as the red light being lit, I also see a different battery indication in the bottom-right corner (this is on my PRS-650). Instead of the usual indication of the charge level, it shows an arrow into the battery to indicate charging. As you say, the red light goes off when fully charged. I've never checked, but I'd guess the bottom-right battery indicator would also change back to normal once fully charged as well.
I believe there may be some kind of issue that means it shouldn't be charged from a sleeping laptop? Not sure on this, but there have been other threads that discussed it - I could have the wrong end of the stick on this, and I'm sure other forum members will be more knowledgable than me on it.
Personally, even before I heard of that issue, I've always charged it on the laptop only while actively uploading books (or otherwise using the laptop for email and such), and used a mains charger if I want to leave it to charge for a while unattended.
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