The only way to back-save into prior versions is unfortunately one version at a time, in part because the back-save process attempts to give the best representation of any new features and new library objects in the prior release. (Trying to do this more than one version at a time would consume a lot of resources for Graphisoft I would imagine.)
So, yes, you'd have to save to 23, then from 23 to 22, from 22 to 21 and finally 21 to 20.
Depending on how many new feature you have used since 20, you might lose a lot of information. Everyone's mileage will vary.
As for the Revit family object conversion... I've not tried, nor have I read, of anyone trying to back-save a converted object. If the conversion uses GDL features not available in 20, then the objects won't work in 20. Only way to know is to try I suppose unless someone who has tried chimes in here.
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