SQL Server performance and fully qualified table names

Question

It seems to be fairly accepted that including the schema owner in the query increases db performance, e.g.:

SELECT x FROM [dbo].Foo vs SELECT x FR

Answer 1

SQL server will not make an extra look up if the default schema is the same. It should be included if it's not and it's a query that is used a lot.

The database name will not benefit the query performance. I think this could be seen with the Estimated Execution Plan in the Management Studio.