1. The reason why the Diagnostic Server's (or Spotlight User) Total CPU is high is because the Diagnostic Sever is running 24/7 compare to other processes that may not be 24/7. So the Spotlight User will always show higher total CPU.
2. The SQL pane at the bottom is not showing the SQL corresponding to the Total CPU but it only shows the current. The reason why QS_ConnectionDetails.sql shows up all the time is because to get the SQL Activity page, Spotlight runs QS_ConnectionDetails.sql.
If you have second Diagnostic Server monitoring the same SQL instance and if you pull up the SQL Activity page from the first Diagnostic Server and point it to the second Diagnostic Server user, you'll likely see a different SQL - provided of course that the second Diagnostic server does not have the SQL Activity page open too.