Can a table have Both a Clustered Columnstore Index and Nonclustered Columnstore Index?
No, you can't:

CREATE TABLE dbo.cs_test (id INT NOT NULL)

CREATE CLUSTERED COLUMNSTORE INDEX cs_whatever ON dbo.cs_test

CREATE NONCLUSTERED COLUMNSTORE INDEX nc_whatever ON dbo.cs_test(id);


Returns the error message:


  Msg 35339, Level 16, State 1, Line 7 Multiple columnstore indexes are
  not supported.


The same result for multiple nonclustered columnstore indexes, as well.