I'm always amazed at how many people seem not to understand the following: A "background check" is nothing more than a report regarding someone or something. It can be as detailed or as sparse as the persons requesting the report and conducting the underlying investigation want to be.
That being the case, the answer to your first question is that it goes back as far back as the person requesting it wants to go, and the answer to the second question is maybe.
Putting aside whether this person has the necessary expertise on the subject, I assume that he or she was speaking to two things: (1) the practices of the company by whom he/she is employed; and (2) what is allowable under Washington law in a particular context. These are different things that what your initial questions asked about.
Even if any of these things were to show up on a "background check" relating to your efforts to obtain employment with a non-governmental employer, I can't conceive that anyone would give a rip about things that occurred 29-37 years ago (although someone might conceivably ask about the reason for the "other than honorable discharge"). By way of an anecdotal reference, when I was 17, I pleaded guilty to two misdemeanors after being charged with a felony. When I sought admission to the State Bar at the age of 33, I disclosed this (even though I probably didn't need to since it was a juvenile matter), and it didn't raise an eyebrow. IMO, your stuff is even more trivial.
I think that's almost certainly true.

