I have a server running on a Compute Engine instance that makes requests to an AppEngine application (in the same API project, FWIW). Did I charge "outgoing bandwidth" for data coming from the AppEngine app?
Yes. If you have a GCE instance and a GAE application talking to each other, you will not be billed for the incoming or outgoing bandwidth for GCE , but you will be billed for the outgoing bandwidth from GAE .