Does the solar hot water stay hot even during the night?

Yes, water is stored in a well-insulated tank. In the event that there is not enough sun to produce hot water, electricity can be utilized to heat your water.

Your water will stay hot for a period of time after the sun goes down.

Unless, in the rare case, there is long periods where there is inadequate sun exposure you will be able to harness solar energy on your energy consumption!