The question does even X know Y? Implies that X is somehow out of touch, and not knowing Y, but maybe they do - surprise!
The question Does even X not know Y? Implies we would expect X to know Y, but what if even X does not?
The question Doesn't X even know Y? Implies that X is stupid and doesn't know a lot of things, but can it be that they are so stupid that they don't even know Y!?!?
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The question Does X know even Y? Implies they are knowledgable about a lot of things, but Y is such a rare and mysterious subject that we would be surprised if they did but what if they do know Y!?!