Public-facing apps are temporary. Wherever possible, try to create static data resources from dynamic databases by pushing JSON to AWS S3, cf. White House Visitor Logs. If possible, use AWS Lambda to handle incoming data. If all else fails, use a library like django-bakery.
For temporary apps, we can provision Elastic Beanstalk and EC2 instances on our separate Interactives AWS account.
We maintain a production database in AWS on a separate Amazon account owned by the Interactives Team. It is an AWS RDS t2.medium instance running PostgreSQL 9.6 with automated backups going back 14 days. We do not have a hosted staging database at this time.