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If you want to restore the previously used standalone window to manage search engines then you can toggle this pref to false with a middle-click on the about:config page.

about:config page: browser.search.showOneOffButtons = false

You need to close and restart Firefox to make this work properly.

In the address bar, type about:preferences#search<enter>

If you miss being able to switch search engines without going crazy with menus, try this out;

Context Search {web link} Expands the context menu's 'Search for' item into a list of installed search engines, allowing you to choose the engine you want to use for each search.

You only see two suggestions of search terms that you typed if Firefox also displays suggestions provided by the search engine website. I see the full list if I press the Down key without having typed anything.

If you want to see more typed search terms all the time then you can disable the suggestions via "Change Search Settings" (Options/Preferences > Search)

I don't know what happens if the suggestions aren't working properly for some reason or if the selected search engine doesn't provide search suggestions.