I see the battery is strapped (mounted)...
I see the battery is strapped (mounted) to the stem in the picture; my bike has a very short stem, to short (73mm/28 degree) to mount a battery to it. Does the system have a cord long enough to strap the battery to the top tube or a bottle cage?
No, the cord is pretty short. Mine fits on a 90mm thompson stem. If you have a real shorty on there you'll have to work out something else. There are cord extenders by niterider I think.