Re: Plz, help decipher one Job Application...
I think the question is whether or not you were meant to see the contents of the fax. If it came in on a generic fax machine which everyone has access to, then there is no reason why you shouldn't show it to your boss and say "This is very strange. There aren't any jobs in our department being advertised, are there?!" in an incredulous voice.
If you don't work for the HR/Personnel department, then I don't think you should contact the writer of the letter asking them anything.
It shouldn't be too difficult to find out if a job in your department is being advertised, surely. Just Google "Job/Employment vacancies at [company name]". Almost all job ads are online these days.
You could go down the other route, of course. If you don't think anyone else saw the fax, just shred it!
As far as my opinion about the letter is concerned, I would assume that it's just someone sending their CV etc to every relevant company. Anyone applying for a job knows that you start your letter with "I would like to apply for the position of [job title] as advertised in [name of publication] on [date]."
Remember - correct capitalisation, punctuation and spacing make posts much easier to read.