Historically both fascist governments and fascist movements require external attack to collapse - or a succession crisis, which takes a while. And a lot of people can get killed along the way.
As for ending up attacking each other I think that is a general authoritarian thing with purging to take/secure power - it happens with communism and it happened with monarchies.
One interesting outlier along the lines was Fascist Spain. It was caused by a chain of events caused by internal attack of fascists for their own cynical reasons. [https://en.wikipedia.org/wiki/Assassination_of_Luis_Carrero_...] Combined with a secret liberal king, Juan Carlos and the power was used to restore democracy.
No it wasn't. The economic recovery occurred way before the war did.