He may have been extremely conceited and believed he could survive such a loss, or alternatively, thought the Ring was lost, not destroyed. Such may have happened if the Ring fell into the Sea, or fell into lava that wasn't hot enough.

:For that matter why did all of Sauron's power disappear
:when the ring was destroyed

Sauron placed a large part of his soul within the Ring, magnifying his power. When the ring was destroyed, his soul was ripped asunder and all of his soul that he placed in the Ring was destroyed.

:(I should also like to know if the destruction of the ring
:killed Sauron or simply made him helpless

He'll regenerate himself again, but as a "shade of malice that gnaws itself in the dark". Never again would he have much power.