Yes they do...But in a different way because they don't close their eyes when they sleep. You will only know that they are asleep when they stay still in the water. Turning off the lights is recommended but is not that necessary.
No you dont have to turn of the light for the aquarium. i turn mine off and there still swimming around like always. they sleep when they want to. They sleep without moving just floating in the water
They do sleep ,but not necessarily at night. Turning off the aquarium lights at night allows the tank to return to a normal temp. without artificial heat and prevents algae growth.
it helps if you turn the light off but they do sleep. its more like taking naps. if you ever catch them just hanging out and not moving like they usually do then its having a nap. some fish like bettas like to sleep resting on things so plants they can rest on are always good.
no you don't have to turn off the lights.because fish do not have any eyelids they sleep with their eyes open.To know if they slept or not you have to check whether they are moving or not.
Sounds like a good idea. If nothing else, it would save electricity. I don't know about their sleeping habits, but they don't even have eyelids, so a little darkness might be a good idea.