the bands are for clamping the light on to different sized bars.
The battery case straps its self to the frame due to its length. The rings as far as i can see are to open the velcro rather than extra straps.
Dont ask me about the battery – i charged it first time till it flashed and then used it. I have just go a new one and will do the same and will just use it and charge it then take it off charge. Probably totally wrong but for the cost and the use it gets who cares, ill get a new battery in 6 months if i need to!
Top tip, if you have a Giro Hex or similar with central channel of vents the light seems to fit perfectly in the channel and clamps to a bridge in the channel securely. No need for a helmet mount. This is how i use mine rather than on the bars.