Over the pass few years much has changed for data structures within Appian, specifically with record types and custom data types (CDT). There does not seem to be any official documentation on how to convert an application designed using CDTs to one using records. While CDTs have not been entirely fazed out but rather relegated to support with plugins and smart services, it is often more performant and (based on Appian documentation) preferred to build using record types.
My questions are:
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For #1 - I would say that the main benefit is that Record Types could help you simplify your app so it could help with maintainability in the long term if you often have to make changes to the application. Otherwise, the only benefit could be some performance gains.
Here is a comprehensive list of all the features enabled by data sync: https://docs.appian.com/suite/help/24.1/records-data-sync.html
For #2, as the others have said, I would refactor portions of the app as I touch them.