"How do you save a search in a non-personally identifiable way?"
To a first approximation, you just... do it.
Granted, if you search "{jerf's realname here} {embarrassing disease} cure" or something, in the pathological case, you could at least guess that maybe it was me, though even then my real name is far from unique, and nothing stops anyone else from running such a search.
But otherwise, if all you have is a pile of a few billion searches, you don't have any information about any of the specific searchers. Even if you search for your own specific address, you don't really get anything out of it; there's no guarantee it was you, or a friend of yours, or an automated address scraper. There isn't much you can get out of a search string without more information connected to it.
The rest of your criticisms are too powerful for the topic at hand; they don't prove we shouldn't use DDG, they prove we shouldn't use the internet at all.