How professional should my query for a PostDoc position be?
When asking about possible PostDoc positions what would be a good grade of professionalism? How long should the mail be and what should be included? (merely asking if somebody knows something would only take a line or two)


Obviously you want this to be professional (e.g., "Hey dude, I need a job" isn't great in any case), but not necessarily very long or formal. Your milage on this will vary based on the discipline, geographical region, and the individuals involved. However, in STEM fields and assuming this is a professor in the US or Europe, I would opt for an extremely short and informal mail to establish first contact.

Dear Prof. Farnsworth / (or: Dear Rupert, if you are on first-name basis)

as you may know, I plan to graduate in summer and am currently evaluating postdocs options. Given our joint interest in FTL travel, I was wondering whether there could be any openings in your lab that would fit my time line. Alternatively, are you aware of any postdoc stipends or grants that we could jointly apply for?

Thanks a lot in advance,

xLeitix

In my experience, such a super-informal mail has the highest chance of actually being read and is entirely sufficient to get the discussion going. Let the prof. decide what documents, if any, he actually wants to see before progressing (letters, CV, just a link to your Scholar page, etc...).

Important disclaimer: this really only works because the OP has stated that he assumes the potential postdoc advisor will recognize him when he receives the mail. If you have never met the person, or suspect that he won't be able to match your name to your face, add at least a link to your website. If you don't have a website, build one before doing anything else related to your job search.