No. Calyxes do not produce pollen. Pollen sacs and nanners do. Nanners are properly called anthers, and they are the pollen producing parts of male flowers. Pollinated female flowers cannot produce pollen.
Sometimes. But if you smoke enough of the seedy stuff you will wake up in a pair of striped bellbottoms with black light posters all around you, with Steppenwolf playing in the background and your friends will all tell you it's still 1971. This actually happened to a friend.