Problematic Volcano affects only the declaration of blockers. Creatures can still be put onto the battlefield blocking creatures on the other side, abilities of creatures can target creatures on the other side, and so on.

If a creature somehow has no side chosen for it (perhaps because it’s not normally a creature but becomes one temporarily, or because Problematic Volcano’s enters-the-battlefield ability didn’t resolve) it can block and be blocked by creatures on either side.

The designation of left or right matters only for one Problematic Volcano. If another enters the battlefield, the designations for the first won’t matter.

While choosing sides for their creatures, each player will know the choices made by players before them.

If two or more permanents with the world supertype are on the battlefield, all but the most recent one are put into their owners’ graveyards. In case of a tie, all are put into their owners’ graveyards.