No, unfortunately, they need to be in direct sunlight for at least some of the day to work.
              
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No, not all of the lights have a sensor. All lights with a sensor have that noted in their description.
Depending on the settings, most of the lights will come on at dusk and turn off at dawn if sufficiently charged.
No, you do not need to plug these lights in to charge the battery. They are all powered by solar (sun) light.
No, unfortunately, they need to be in direct sunlight for at least some of the day to work.