You may find this white paper useful

You may want to cross check the column mappings. Please refer this article

After much digging, what I found was that the new active cluster ( first time it's ever failed over ) had a different level of SQL 2005 and did not...

You may also read the Default Trace during the time the user loses his permission.

Cross post

Even I feel that the job does some shell commands. May be like the cmd window which is expecting a response.

I assume you are trying to take the backup using SSMS and the destination is referring to the old location.

Why not use this query instead of using the GUI?

BACKUP DATABASE...

Microsoft documentation reads as below.

Increasing the timeout value from 10 to 30 will ensure that the mirror monitor will ry for 30 seconds before throwing the time out error.

As discussed earlier, please schedule a transaction log backup job. This is the permanent fix

I assume with indexcol you mean the columns referred in an index. Refer this link for more details.

Do you see any error messages in the Application\System Event logs?

From the error message it is clear that there is memory contention on the box. Is the server hosting only SQL Server or any other application? Also try running the...

Placing tempdb files on different drives is beneficial. Configuring the MAXPDOP/ using the MAXDOP hint depends on the requirement and the hardware capabilities.

This is what the MSDN documentation states.

you can use all backup and recovery models with FILESTREAM data, and the FILESTREAM data is backed up with the structured data in the...