So information has no real definition in physics. You can encode information like a telegraph signal moving down a wire but if their is no interpreter on the other side who knows the code than it is the same as a random series of pulses. Next is your 0 K question. The answer is it depends. If you have information coded chemically or some other physical way like written word than no. It would survive being at zero however any communication is impossible as nothing is moving. Of course it is impossible to get to true zero so kinda a moot point.
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