Stick Up Cam - battery/plug-in questions

Looking at getting a Stick Up Cam but not sure about getting a Plug-In or Battery. \* Can you add a power adapter to a Stick Up Cam Battery? Would it charge the battery and use it if power is out? \* Can you add a battery to a Sitck Up Cam Plug-In? Would it charge the battery and use it if power is out? I assume the Stick Up Cam Plug-In does not come with a battery, right? Finally, is the battery these use the same as the Spotlight Cam Battery? TIA.