As far as I'm aware, a lot of the safety critical certification requires the entire stack to be certified, in which case the OS (which would probably be a hard-realtime OS) would be certified too.
Probably part of the $100M price tag is a hefty license fee to use said OS.
Yep, unfortunately I don't know which OS they went for but it was one of the commercially-available RTOSes on the market. Those don't come cheap.
Avionics software certification is phenomenally expensive. Both Airbus and Boeing have warned in recent years that it has become such a big part of their development costs that they're concerned about it becoming unsustainable.
Probably part of the $100M price tag is a hefty license fee to use said OS.