Are all animals showing positive phototaxis diurnal? Are all animals showing negative phototaxis nocturnal?

Answer 1

Mostly yes, but not all of them. The clearest example is moth. They're nocturnal, but they're attracted to light. Some animals live as nocturnal because they can find more food (less competition with other species) and less predator, not because they're repelled by the light.
For diurnal animals, I can't give any example for negative phototaxis animal. Maybe the blind animals in dark caves or ocean depth? I don't know if any of them is diurnal. Sorry.

Answer 2

Many types of small marine invertebrates that are nocturnal in habit are attracted to light. If you hang a bright light over the side of a boat at night, either in the water or above the water, swarms of them will accumulate in the lighted area.

Answer 3

Yes