The "general purpose"
search functions incredibly well, from what I can tell. Again, comments in order of your query.
- Haven't used it often enough, tbh. But that's just me being disorganised.
- The drop down menu complements the overall organisation of the site nicely.
- Eh ... thinking still ... well, I don't want to conjure up grievances.
- As said, I should be using it more for the search it is already.
- Well, it is already omnipresent through the site and prominently displayed. Perhaps that's why it doesn't always register with me, I'm too used of it being there. By no means I am advocating that the search should be harder to find, btw!
Perhaps a "similar or related material" option of some kind could work - you could try to fashion out an associative search. Often, when interested in an unfamiliar subject, one doesn't really have a good handle on applicable search terms. Since there are experts of various fields here, perhaps some could volunteer to group laymen's and professional's terminology so as to specifically provide a shortcut to in-depth material outside one's direct knowledge.
In effect, an "associative" search would draw up something useful beyond the search terms, often the ultimate objective of doing a search in the first place. Especially in technical matters. There are also a number of academic and professional search engines, maybe you could make use of those as well.
"In theory there's no difference between theory and practice. In practice, there is." - Yogi Berra