Everything lives on the keyboard itself. The app just configures files on the device, basically. The keyboard also works without the app of course. This approach has the added benefit of making your configuration portable. For example if you remap your dial, and move to a different computer, your remapped dial will persist.
There are a couple of small quality-of-life features that do require the app: for example if you want haptic feedback when you receive a notification. This is because the keyboard has no idea what is happening on your OS, and requires some middleware. But all the core functionality requires no app at all.
To answer your second question, the firmware for Altar II will be open-sourced, as the firmware for our Altar I keyboard is. You can see the Altar I firmware source code here: https://github.com/electronicmaterialsoffice/firmware-altar-...
Both Altar I and Altar II firmware are based on the open-source ZMK (https://zmk.dev). We try to contribute back to ZMK whenever we can because we have benefitted so much from it. Two members of our team are also long-standing ZMK contributors.