The SQL Server Native Client is an MS client to connect to SQL Server through the OLE DB/ODBC interface. It's version must correspond with the SQL Server DB you are trying to connect to. QlikView doesn't mind what version you use, as long as it adheres to the OLE DB/ODBC spec.
Newer Native Clients will almost always work with older SQL Server versions (in contrast with Oracle). There is no separate Native Client for SQL Server 2016. Version 11 will do just fine. Version 10 was released together with SQL Server 2008.
Note that the native client is part of SQL Server, not a part of Windows or MS Office. AFAIK you won't have any version installed by default. Download an installer from the Microsoft Download page and install it on the laptop/desktop where you develop your QlikView documents, and on the QlikView server where you plan to roll them out.
No idea about that driver. I always use the SQL Server Native Client, not the one you are showing in your screenshot.
But as I said before, the driver should correspond with the version of your Database, not with the version of QlikView. So if the default driver (installed with Windows or MS Office?) works with your copy of SQL Server, it will be ok for QlikView.
You can test in Excel whether it works with your SQL Server database.