I am trying to use the application token to access the layers set up for it, but I can't understand where to use the application access token. For example, sending a request like this -
You shouldn't put the application access token into your app, since that would allow anyone with the app to make requests on behalf of your application.
If the layer is public, you can run place/list?layer_id=XXX without specifying the application access token and it should work just fine.