What algorithm does the cert use?

https://docs.microsoft.com/en-us/sql/relational-databases/system-catalog-views/sys-sql-expression-dependencies-transact-sql

Permissions

Requires VIEW DEFINITION permission on the database and SELECT permission on sys.sql_expression_dependencies for the database. By default, SELECT permission...

Key size or algorithm? 2008 doesn't support the same ones that 2014/2016 do.

See the documentation:
https://docs.microsoft.com/en-us/sql/relational-databases/system-stored-procedures/sp-send-dbmail-transact-sql

Can you give a reference for those 'standard' steps for splitting a partition?

Database Encryption keys are not, afaik, limited by edition.
What's the error that you're getting?

Master one of the aspects you already know, is another option

Errr... CROSS APPLY to the function will probably be what you're looking for, but I have no real idea because you haven't given enough details.

If you're using SQL 2008 R2, I'd suggest you stick with trace. While XE existed on 2008 R2, it was fairly limited. It became a lot more usable in 2012.

Always Encrypted is supported on Standard Edition.
https://docs.microsoft.com/en-us/sql/sql-server/editions-and-components-of-sql-server-2016

See the section RDBMS Security

They're not included in Express edition.

You can stop getting it by figuring out what app on the client specified is trying to connect to a DB that doesn't exist, because the root cause of this...