Is it possible to use cross database queries in both Azure and SQL Server 2016?
The 'New Polybase connectors' added in SQL Server 2019 CTP 2.0 give you what you're looking for.  These are new in 2019, and are not in the 2016 and 2017 releases.

See 'New PolyBase connectors' here:

https://docs.microsoft.com/en-us/sql/sql-server/what-s-new-in-sql-server-ver15?view=sqlallproducts-allversions#databaseengine