As JGB146 observed, we are prioritizing cards that you're "involved" with above other search results.
Additionally, if you have a board open, and you initiate the search from there, then results from the board that you're looking at will have the highest relevance (and archived cards will be included in the search results)
I agree with your friend about not dividing up into separate boards by type of job.
With your examples such as 'Design ideas' etc, I think they really do fit naturally within different lists on the same Board. It's exactly the sort of usage that Joel demoed in multiple videos about Trello.
The only thing I can think of, to help manage very long lists, is to use Trello's Labels system to put categories on cards, and then use filtering. You should definitely give meaningful names to the default labels.
Having said that, fairly early on the Trello on Trello board got huge, and eventually they reduced the scope of it. So it's does seem to be a well-known problem.
Best Answer
Subscribe will get you notifications (and emails) on all cards on the board whenever a card has an action on it.
Pin to main menu is a toggle that enables the board to show up in the 'boards' list on the right/top.