Sun
corona
If ozone layer disappears, UV rays will enter the earth. these are fatal radiations of the sun.
The sun is hidden by the earth. It's why the sun disappears at sunset and reappears at sunrise.
Yes, but according to the bible when it disappears we will not need it.
Solar eclipse or blocked by clouds
metamorphosis
It will be impossible for life to exist without the sun. In fact, even before the sun totally disappears, life on earth will be gone. Check this website : http://www.dlr.de/en/desktopdefault.aspx/tabid-1/86_read-18304/
Dusk
If by "disappears" you mean ends its life cycle then, no, you wont be able to see the Moon. Mostly because by the time the Sun is gone the Earth would have been swallowed long ago and we would all be dead!
The time when the sun disappears below the horizon at the end of the day is known as sunset. This marks the transition from day to night as the sun's light is no longer directly visible from the surface of the Earth.
Shadow