The simplest query is:

select * from msdb.dbo.backupset where backup_start_date between <earliest datetime> and <latest datetime>

What information is available in the msdb.dbo.backupset table for the day in question?

If LineNumber is used, it has to be included with the OrderNumber to make it unique.  Also, based on experience, I have worked on some systems written in Fortran and...

It depends.  What are your requirements?  Out of the box, SSIS can not detect changes between databases.  You will have to write the process to identify changes and to move...

I started to ask you to explain why the difference, but I just figured it out, the addition in DATEADD is not communitive.  0 + 107 != 107 + 0. ...

select dateadd(dd, 0, datediff(dd, 0, getdate()))

If you are still have a problem with the restore, have you checked the SQL Logs or msdb.dbo.backupset table to see if there is a missing transaction log backup?

Look at sys.indexes.

Pardon me for this, but I am practicing to be a consultant: It depends.  Since you are using an identity field in the OrderDetail table, the LineNumber column could be...

Adds the silly "TOP 100 %" to a view with an order clause; while this seems to work when you run the query while editing it, the order may not...

Yes, you can.  But if it needs to grow again due to database updates or maintenance procedures, you will take a performance hit.

select convert(char(8), getdate(), 112)

You shouldn't see any real hit on your server during the change.

Have you checked the SQL Server Logs for the day that the full backup, differential backup, and transaction log backups you are attempting to restore were taken?  If no backup...

Just curious, but does the index on the initials need to be unique?  If so, how will the individuals in question know what their unique initials are when you finish...