1. Is it possible for an AWS Athena database to exist in one AWS account and its data files to live on another AWS Account?

A). Yes it is possible

2. How do you know where an AWS Athena table data file lives? And does an S3 output bucket exist?

A. Go to the AWS Glue data catalog, go to a specific Table, and check "Location", which provides information on a file location.

3. Is there a better approach to finding this problem's root cause other than the trial and error approach?

A. Run the query directly in the Athena console to check for errors. This step can often reveal if permissions or configurations are missing.

The other way is to check CloudTrail Logs and enable Verbose logging in AWS Wrangler to check the issues.

Please let me know any other information.