SSIS and MSDB Packages in a Clustered Environment

There seems to be a lot of confusion about SSIS administration in a clustered environment, and I think a lot of it comes down to SQL error messages that occur in a variety of situations.

Take the following, when browsing the MSDB stored package folder when connected to an SSIS instance:

The SQL Server instance specified in SSIS service configuration is not present or is not available. This might occur when there is no default instance of SQL Server on the computer. For more information, see the topic "Configuring the Integration Services Service" in Server 2008 Books Online.

Login timeout expired
A network-related or instance-specific error has occurred while establishing a connection to SQL Server. Server is not found or not accessible. Check if instance name is correct and if SQL Server is configured to allow remote connections. For more information see SQL Server Books Online.
Named Pipes Provider: Could not open a connection to SQL Server [2].  (MsDtsSrvr)

Login timeout expired
A network-related or instance-specific error has occurred while establishing a connection to SQL Server. Server is not found or not accessible. Check if instance name is correct and if SQL Server is configured to allow remote connections. For more information see SQL Server Books Online.Named Pipes Provider: Could not open a connection to SQL Server [2].  (Microsoft SQL Server Native Client 10.0)