I need pull data from "Google Sheets" and "Analytics", for which I'm creating a connector, and I would like to know if it's possible re-use existing "Google Analytics" & "Google Sheets" provided by DataStudio.
Re-using native connectors inside a Community Connector is not possible at the moment.
However, you can achieve the same result by using Apps Script Advanced Services. Most of the native connectors in Data Studio have a corresponding Advanced Service in Apps Script.
For your specific use case, you can use the Analytics Services and the Sheets Service. Before using them in your code, make sure that you follow the instructions to enable the advanced services. The Fusion Table Community Connector is an Open Source example that shows how to use an advanced service in a Community Connector.