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Questions 1 and 2, the answers are stored within the workbook/datasource file itself and aren't exposed as metadata where you can query them in postgres.
There are some third party tools that can pull this out, like Power Tools for Tableau: http://powertoolsfortableau.com/tools/desktop/
You could also write your own program using the Document API: GitHub - tableau/document-api-python: Create and modify Tableau workbook and datasource files
Question 3: You could deny permissions to download underlying data, but I don't think there is a way to allow it,but limit it.
Question 4: Here you go Upgrade
Appreciate your reply!
I have very little / No understanding of Rest API or Python and might again knock the Forum doors for assistance. Though the links and information you have supplied helps!