Yes, you can just install the patch only on the UAT instance of SQL server.

Also in SQL 2005, you have to perform the patch installation from the active node. In...

Right fill factor will definitely help...but ensure to test the fill factor value. if the fill factor value is too low eg. 50% then the number of pages taken to...

Yeah, most of points above are correct. Some clarifications:-

SQL Server 2005 uses task scheduler service to install the patch on the remote node as well. SO you don't have to...

It seems the issue is specific to SQL server 2008..I tried it on SQL server 2005 and it worked just fine:

CREATE SCHEMA DBA

ALTER SCHEMA DBA TRANSFER dbo.myTable

ALTER SCHEMA DBA...