Is there a streaming API that can be used to pull data from my Google Analytics custom reports into a separate dashboard interface? If not, could I set it up to automatically push data to update the separate dashboard on a daily or weekly basis? I see that I can set up automated emails with data exported in Excel or CSV format, but this option would still require me to manually upload and refresh the data set on a regular basis.
there are no straightforward streaming API. But most data for a regular reporting could be accessed via Reporting API (https://developers.google.com/analytics/devguides/reporting/). Popular solution is accessing Google analytics data from Google sheets with Apps Scripts and updating these data with shceduled scripts. (https://developers.google.com/apps-script/advanced/analytics)
For streaming solutions you coudl check Owox pipeline (https://www.owox.com/products/bi/pipeline/google-analytics-to-google-bigquery-streaming/)