Are there database backups? If so, how long are the backups supported?

Automated backups of the database on each environment are made every minute. These backups are kept for a period of 35 days, enabling you to restore your website database to a desired point in time within that period. You can request a restoration to a point in time by contacting the Sitefinity support team.

If the Developer Extensions toggle is enabled, Sitefinity Cloud environment databases are automatically exported to .bacpac files on a weekly basis. You can access these files and use them to restore the database locally for development and testing purposes. Databases can also be exported on demand. 

For more information check out this database documentation.