I am building a Node.js Analytics dashboard that includes internally generated data, and would like to add Charts from our Google Analytics. 1/ What is the right Google Analytics API to do so 2/ Is there a node.js package to embed the chart itself (rather than retrieving the data from GA and then having to build the chart myself)?
You'll want to use the Core Reporting API to pull data, and you could try Google Chart Tools for creating your graphs.
Check out EmbeddedAnalytics.
While not a node.js solution, we are a 3rd party solution (using the Core Reporting) designed specifically so that you can avoid the heavy lifting of "retrieving the data from GA and then having to build the chart myself" as you have said yourself.
The process is very simple.
<iframe> tag where the chart is to display.