Silpion

This plugin gives a possibility to manage Frequently Asked Questions as a custom post type. Site admin is able to add and edit questions and answers, assign them to categories and then display the output on any page using [faq] or [faq category={{category_id}}] on any WordPress page.
You can embeed the FAQ directly in your code using lcb_faq_display() function.

LCB FAQ

Displays questions with answers with FAQ category column.

Evgeniy Kutsenko

This Plugin allows you to include a simple Textbox through which your site visitors can ask you short questions. 
You can answer them through the backend. 
This plugin is not a dependent version of the plugin <a href="https://wordpress.org/plugins/askme/" rel="ugc">Ask Me</a>.
See it in action at: (<a href="http://wp.starcoms.ru/qa-plugin/" rel="nofollow ugc">http://wp.starcoms.ru/qa-plugin/</a>)

Simple Q&A

Simple Plugin to let your users ask questions.

LCB FAQ vs Simple Q&A