I saw this post was never answered.
Do you know of any extension or script that allows scheduling data exporting from Data-Studio to G-drive?
What I have tried:
I create a table of fields, but I see no way to schedully export it just on off export.
No, but you can schedule to send the dashboard by email.
Data Studio is a visualization tool, you should not expect advanced export features.
If you use BigQuery, you can connect your Google Sheets direct to your data source. And if you don't use BigQuery, you should try.