Creating custom Wordpress object

I'm putting together my own Wordpress theme for a very specific set of client requirements. I'm fine with front-end theme work, but I need some help with back end.

The task is kind of like a support site, with lots of Q and A's. I'm building a support site for a company, which means most Pages will be populated with many questions and associated answers.

The page Structure would be something like this:

Home Page (with links to Most recent Q+As added) and common sections
-How to use the app (10-20 Q+As on page)
-How to manage integrations (10-20 Q+As on page)
-Other page (10-20 Q+As on page)
-5-10x 'Other pages'
About Us
Contact Support

Requirements and my comments

-Each Q and A does not have it's own URL
This makes using Posts for Q and A's unattractive.

-Each Page is made up of a Table of Contents which allows quick scrolling to questions
An ideal solution would be some code on the page theme template which grabs each "Q and A" object within a certain category/section/identifier and load it to the page

-New questions and answers can quickly and easily be added
The ideal solution for support reps is that they can add a question and answer, and assign a category, rather than edit a huge page of questions.

-Order of Q and A's on page is important
Ideal solution should allow you to order the Q+As within their given category/section/other.

-On the home page, most recent Q+As added list exists

-Each Page of Q+As has a "last updated" date, which is the date the most recent Q+A was most recently modified.

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Ideas I had

Posts or custom posts seemed like a good idea, but they create permalinks. But my "Pages" would actually be Category Archive pages. We don't want a Q+A to be be assigned two categories. Also, custom post ordering seems difficult. If we could suppress permalinks and ensure on category or section and find a way to order them - this could work.

FAQ Plugins

It seems like these all are a bit clunky and the amount of custom dev to re-skin on it might not be worth it, might be easier to do something totally custom.

Question:
does anyone have any ideas how this could be achieved?

via Chebli Mohamed