Works for me on 78.6 ESR.

Whether the page is opened in new tab or current tab is controlled by Firefox. You may toggle `browser.search.openintab` in about:config to make it behavior as you like.

The behavior is introduced clearly in the description. Just read the description so you wont be confused then. I cannot understand why someone does not have time to read it, but are willing to have a try and leave a even longer comment here. Basically, this is what WebExtension (extensions for Firefox 57+) may done currently. If you prefer a fx24 like search bar, you would be better to switch to other browsers.

It sets default search engine list based on your browser language setting. The default search engines only used to initial your search engine list and fill it when you try to reset your settings. You may simply delete any of them as you like. I had a double check about the initial search engine list. Only two Chinese search engines (and some common search engines in Chinese language, including Amazon and Wikipedia) are included here. If your browser is configured as simplified Chinese, baidu would be included; If your browser is configured as traditional Chinese, readmoo would be included. If not so, it should be a bug. You could report any bugs to me. But please include your browser language setting so I can debug it.

Anyway, this extension is free and open source. You are welcomed to fork it and develop another extension for whatever you want. We would be happy if someone like you would create a better extension for this use case. Only remember that this extension is published under MPL-2.0 if you do so.

This extension do not collection anything from your browser / computer. And even do not trigger a single network request it self. The site named `6905b838-e843-4ee3-9df0-b4c79673b21c.invalid` is literally _invalid_ and no one may hold that site. Your search words will only be sent to the search engine you configured in the extension but not any other servers. Extension come up by some default search engines to make it easy to use. The default search engine list is decided by your language settings, and the list is based on Firefox built-in search engines. If you dislike some search engine given in the list, you may just remove it in extension settings by one click.

使用您想添加的網站搜尋任一單詞，如「ABCDEF」，在搜尋頁面的網址列中找到被搜尋的單詞，將其替換為 {searchTerms} 即可填入設定中。
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使用 POST 方法的網站請參考這篇文章：https://github.com/tiansh/classical-search-bar/wiki/Config-POST-Search-Providers
因為現今很少有網站還在用 POST 方法，所以這個功能並沒有展示出來。
這裡有針對這兩個網站製作好的設定檔，https://gist.github.com/tiansh/5576f4d361c3ef919156e4babf1c95b1 你可以下載之後選擇「匯入並追加」添加。

This extension aimed to switch default search engines quickly without open browser preferences by about 5 clicks, and let you know which search engine is currently selected without open the search pop up. You are kindly welcomed to uninstall it from browser add-on manager if you do not need this feature.

The button added by web extension may only response click / contextmenu events. And it is not possible to handle mouse scroll anyway. Sorry about that.

This extension may not read your browsers searching configuration. And you had to add each search engines in the setting page. So, adding any search engines to default one-off list will not adding them to this extension.

Importing / Exporting had been added in version 1.3.0.

感谢支持。
这个扩展设计就是要加一个快速切换搜索引擎的按钮。所以暂无改动右键菜单的打算。（这个功能无论从复杂性上还是从和这个扩展功能的比较上来说，完全像是再做一个扩展了……）而且实现右键搜索的扩展已经有五六个了，效果上也大同小异，所以也没必要再多一个类似的东西吧。
火狐原生在右键菜单里面有一个使用默认搜索引擎搜索的菜单项，如果把这个扩展配置成默认搜索引擎，这个搜索也会遵守你在扩展中选择的搜索引擎。（当然，拖拽文本到标签页栏/地址栏也是可以打开搜索的。）
如果实在需要在右键菜单里面选择多个搜索引擎，建议还是试试别的扩展，毕竟主要面向的功能还是不太一样……如果两个扩展在兼容性上有任何问题，欢迎告诉我，我会尽量处理。
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另外，这有个我的右键菜单搜索的扩展，欢迎使用：https://addons.mozilla.org/zh-CN/firefox/addon/simple-context-search/