Why did Schallenberg resign ?
He doesn't want to be ÖVP leader and thinks the Chancellor should also lead the ÖVP. Nehammer is much more of a party machine guy than Schallenberg. It would be strange if one were party leader and the other Chancellor. Essentially, with Nehammer now leading the ÖVP, the party shifted back from "turquoise" to "black", into the hands of the old party elite of which Nehammer is part.
Exactly. Schallenberg was never an ÖVP politician but a 'Kurz politician' - big difference. Now that the Kurz experiment has failed, there is no foundation for him to continue as Chancellor. He may become Foreign Minister again but the ÖVP is back in the hands of the old party establishment.
Obviously, there is no reason for snap elections. There is still a solid ÖVP-Greens majority to support the new Chancellor.