Hello.
The mode button will be the same button you use to turn the lights on and off, if you gently hold down the touch button you will start to see the light change modes.
these will charge on however much sun they recieve, so the battery will charge, but they may just have a lower run time as there is now powersaving mode. So do keep this in mind.
The star comes with it's own battery installed.
Hi,
The light comes with a pole and stake, so we don't see why you wouldn't be able to ziptie it. Just make sure the panel is in a space it can gain enough charge to keep the light on!