There are actually more gods than are listed, the list may expand if there's enough demand for it so having a small, weak god in her basement is fine. We'd mechanically treat it like a Summoned Familiar for Abilities and Powers if they were to be used in combat.

You will need to work up to the business, we recommend saying she's working on getting it together or the like. The business notoriety reward is fairly low, and you can always add the airship aspect to it later so it shouldn't take you too long to at least get it running, especially if you don't spend your initial 25 starting Notoriety.