On #1: smart people have looked for atomic or subatomic events that could make our consciousness non-classical. They've found none. As far as I'm concerned, this is a dead hypothesis. But of course others may disagree.

On #2: not to put too fine a point on it, but all the evidence says death acts just like damaging part of the brain - it stops working - only applied to the whole brain. The thought of some consciousness persisting in the absence of all known function is rather horrifying, now that I come to think of it that way! Happily, we have no reason at all to think it's true.