The "search bar keeping your previous search term" issue has to do with the ownership of the search box. It used to be, when tabs were
below the search box, that made sense. You'd be using the
same one search box no matter which tab you were on, and thus it would always keep the same search term between tabs.
Now, with tabs-on-top, each tab contains its own search box. These should be unique, just like each tab has its own URL bar. It doesn't make sense at all that search queries are preserved between tabs. But that's the way Firefox still does it.
(Thinking about this now, I guess that's a different issue than the one you were talking about... why any search box saves any query after pressing "Enter". Still an annoying little quirk though.)