Hamlet 3.4 The Death of Polonius

In this scene from Hamlet, a cry for help alerts Hamlet to someone behind a curtain, whom he assumes is Claudius. Polonius is unexpectedly in Gertrude's chamber, leading Hamlet to stab the curtain in hopes of killing Claudius. Hamlet desires to kill Claudius during a sinful act to ensure his damnation. The phrase 'dead for a duckett' suggests a bet on Claudius's death, with a duckett being a gold coin. Polonius, even in death, confirms his demise.

What assumption does Hamlet make about who is behind the curtain?

How does Polonius confirm his death in the scene?