WenZe

Category Parent Children Selector is a WordPress plugin that helps you in selecting parent-children categories.
Features include:
<ul>
<li>Button to select all categories. </li>
<li>Button to select all categories including children categories. </li>
<li>Button to select first level of children categories only. </li>
<li>Button to select parent and all its children categories under its sub categetory. </li>
<li>Auto select parent categories when a sub category is selected.</li>
</ul>

Category Parent Children Selector

Helps you in selecting parent-children categories.

MyWebsiteAdvisor

ChrisHurst

Use the [children-excerpt] shortcode where you want to display the excerpts of the child pages. 
Defaults to the first 50 words, can be overridden with length attribute so your excerpts can be set to any length of your choosing.
Developer Website: http://MyWebsiteAdvisor.com
Plugin Page: http://mywebsiteadvisor.com/tools/wordpress-plugins/children-excerpt-shortcode/
Video Tutorial: http://mywebsiteadvisor.com/learning/video-tutorials/children-shortcode-plugins-tutorial/
Requirements:
To-do:

Name: Children Excerpt Shortcode

Use the [children-excerpt] shortcode where you want to display the excerpts of the child pages.

Category Parent Children Selector vs Name: Children Excerpt Shortcode