How do I customize the search box in the navigation toolbar?
How do I change the default search engine for the navigation toolbar search text box?
Alla svar (2)
there is drop-down click on a search engine and it becomes your default search engine.
Want to move things around, use drop-down, at the bottom is Manage Engines, you can add, remove, move up/down/drag engines to change placement.
Want to get more search engines you can use MyCroft or the manage tool, but I think you would generally be better of the the extension "Add to Search Bar" to add a search engine, right-click within a search form and choose "Add to Search bar", you can add a keyword as well.
For even more flexibility you do not need to add search engines, you can right click in the search form of a search engine and choose "Add keyword for this search" and a bookmark will be created for you, best of all this feature is built-in to Firefox. But there are other keyword bookmarks you can also create for any purpose.