Ok guys thank you very much for the shared knowledge!!!
I think I have a final question left, maybe rephrasing my OP a bit:
Can I use one of these Lithium-Ion batteries, recharging them with the original (Canon) charger, and then it will work and when they run out of power the arduino (or whatever) will shut down and that's it?
Or do I have to use some sort of cut-off circuit to stop power once a certain voltage has been reached to avoid lithium explosion, battery swelling, overheating or any common issues?
Unfortunately I tried to research open source handhelds and other arduino projects and the like but they all use Lipo and the ones that just use "regular Lithium-Ion" don't specify what circuit is used to monitor battery juice left...