1) Yes, the API does support managed configurations. You are required to create an enterprise policy first and then within that policy you can create an ApplicationPolicy where you may configure permissions and managed configurations. This can be done using either of the available managedConfiguration or managedConfigurationTemplate properties. In the case of using managedConfigurationTemplate, you'd have to provide the template id created using the managed configurations iframe.
2) ApplicationReport reports pre-defined application data as seen on a particular device where it is installed. Application is a general application info resource where one can find about the app's permissions and managed properties available. Custom, app specific data reporting is not possible in the current (Jan, 2019) API version. Your app would have to implement its own mechanism to send such data to the EMM console, e.g., push notifications, etc.