Not really. Just charge it normally. Freezing it won't do anything but waste your time, which you could've used to actually charge it.
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You can't update a psp without a working battery. It'll state that the battery is low and you need to charge it.
Yes you can, the PSP battery will continue to charge even when you are playing. I would not recommend to do that, it is better if you leave it to charge and then play.
You might need a new charger or battery.
Good question. Charge it for a full 24 hours before use so it gains full battery
you turn it off, cause if you leave it on the battery will burn.