Yes, you can run it from SSMS.  Just be sure that the log backup you create is stored with all the scheduled log backups as it becomes part of the...

Depending on how quickly the client wants the backup depends on your course of action.  If they can wait until the 8:30 log backup to be taken, you could start...

Having just restarted my laptop and running your query in a couple of my databases after minor changes (database name) I get no results which is what I would expect...

Incomplete information, what is the query you are running to get these results?

Have you looked at all you error logs?  What do they say, if anything.
On another note, since we can't see what you see, not much we can do to...

Fix appropriately for the local database, what does it return?
WITH UsedNumbersLS AS (
SELECT
  clnum
  , clname1
FROM
  OPENQUERY([ELITE],'SELECT CAST(clnum as INT) as clnum,...

And isn't fun when people ask for help but can't show you anything?

Well, not being able to see the query and the execution plan, not much we can do.  There are things to look for, such as sub-queries with DISTINCT.  This could...

Okay, let's implement our own interface over ODBC using cursors instead of using something that has already been built and enhanced.  Wait, sort of sounds what my company does with...

If it is filling up your drive you may need to move the log to a bigger disk.  Also, I agree with the others that you should look at increasing...

Job security?