How can I navigate between editing a report and editing a query?

You will be able to edit queries and reports that you have copied to your My Favorites folder as well as those in the Public Folders. However, you will ONLY be able to save those altered reports into My Favorites unless you have editing permissions in that Public Folder.

You choose to edit a query if the data that you need from the report was not gathered by the existing query and will not be even if you change the report filters. Query filters are defined on the Query Panel.
You choose to edit a report if the data that you need has already been gathered by the query and you just want to present it differently (different audience, different time span, etc.). Report filters limit the values displayed on reports, tables, charts, sections within the document, but they don’t modify the data that is retrieved from the data source. Report filters are applied in the Report Pane.

Please review How to Navigate Between Editing a Query and Editing a Report for details.