Does Azure SQL Managed Instance offer SQL Server 2016?
You cannot restore a backup from a Managed Instance to an on-prem version of SQL Server.  Even if you had an on-prem 2019, it wouldn't work.  During our migration this was one of the things that gave me pause as well, that it was going to be one-way without a lot of work.  

Additionally (as pointed out by David Browne) you can use Snapshot Replication between Managed Instances and On-Prem SQL.  So that is a viable method of migrating as well as the horror that I had envisioned internally of doing bulk ETL from MI to on-prem.  

Also, to answer the question directly asked, Managed Instances offer one version of the SQL Engine.  You can select a 2016 compatibility level for your databases if you need to limit yourself to those features.