hijiri

Add the link to dynamic latest post page, and the Archive page to Nav Menu.
Latest
The ‘Latest’ nav menu create the link to latest post page of Custom Post Type. 
( orderby ‘menu_order’, ‘post_date’ )
When the new post is added, the link of ‘Latest’ is updated dynamically.
Archive
The ‘Archive’ nav menu create the link to the Archive page of Custom Post Type.
This Plugin published on <a href="https://github.com/hijiriworld/dynamic-latest-post-in-nav-menu" rel="nofollow ugc">GitHub.</a>

Dynamic Latest Post in Nav Menu

Add the link to dynamic latest post page, and the Archive page to Nav Menu.

joe_bopper

Adds search box as a choice of item in navigation menus admin area.
Features include:
<ul>
<li>now compatible with the WordPress appearance customizer,</li>
<li>search box available as a choice in the admin area for navigation menus,</li>
<li>as many boxes can be added to a nav menu as one likes,</li>
<li>search boxes can be added as children of other menu items (useful for, e.g., mega-menus),</li>
<li>capacity to change button text, placeholder and css classes from the admin area to each search box,</li>
<li>hooks to modify output (see FAQ and/or code comments),</li>
<li>very lightweight,</li>
<li>in keeping styles, html, behaviour, etc., with wordpress defaults,</li>
<li>works straight out of the box, no configuration needed.</li>
</ul>
<h4>Those wanting to translate this plugin, please do.</h4>
I believe the plugin is in a translatable state and I’ll do everything I can to help in translation. It should be relatively quick as there isn’t much text to the plugin.

Bop Search Box Item Type For Nav Menus

I like the way it behaves like any menu item so you can position and decorate it how you want. Thanks to Joe for putting me right on how to get at the placeholder text.

Nice Plugin

Adds search box as a choice of item in navigation menus admin area.

Dynamic Latest Post in Nav Menu vs Bop Search Box Item Type For Nav Menus