It comes with a battery. No case included for now, but you can 3D print your own with the STL files. Later on we will offer 2 cases (CNC aluminum and plastic).
We haven't done extensive testing or optimizations (i.e. sleep, idle power down, etc.) yet. But with the stock battery of 2000mAh and Pi Zero @ ~80mA idle, it should be around ~20h always on. We're estimating a week of battery life once the optimizations are implemented.
That's fantastic. I read in another comment that the startup time of the Pi is 5 seconds. Could this be optimized further? Afaik most of the startup time of Linux is detecting and initializing the hardware, so presumably this could be significantly optimized when the target hardware is known ahead of time.
I'm also sort of disillusioned with modern computing when I see a video of a home computer from the 80s that you press the power button and it's on (command prompt) before you've even removed your finger!