Re-installing the theme will not overwrite your duplicated theme, nor will it update your duplicated theme. This is one reason we encourage people to use the theme as it is named instead of duplicating them.That and there’s really not a need for duplicating and renaming themes any more as you can make non-destructive edits to the CSS javascript, et al. within the RW Page Inspector.
Your theme styles will be reset when switching from one theme to another. A duplicated theme and the original theme are not the same as RapidWeaver sees it, and thus, even though both themes have the same controls, they get reset as RW thinks they are two different themes. Another reason I advise against using duplicated themes.
Installing a new theme should not delete duplicated themes. If that is happening you’ll want to contact Realmac Support.
As for redoing your settings – to use the new (original) theme you’ll need to do so or continue using your duplicated theme. If you’re having trouble moving over your duplicated theme I suspect Realmac Support can assist you with that as well.