It seems we can get stats at the campaign or promoted tweet level, but I need to link these to app cards to get the creative info behind the stats. Is there a way to do this?

Also, is there some kind of high-level ERD available to help understand the relationships between different types of objects such as campaign, promoted tweet, line item, app card etc.

The only stat tied directly the to card object is responses on the Card, as explained here.

For other metrics, you can run a stats request on the Tweet ID that contains the Card.

There is information on the relationships between the mentioned objects on our Getting Started page.