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.
Corrupted storage is a pain :( The Beepberry firmware can safely shutdown the Pi before disconnecting power, so hopefully that will help with SD issues. raspi-config also has a read-only overlay filesystem option now.
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).
The dial/hangup buttons map to modifier keys and power control, and the trackpad can be mapped to mouse/arrow/scroll keys. No plans for touchscreen yet :)