@imjscn you’re absolutely right, “adding something like gravity forms” plugin will be needed for frontend posting by users. although it is a premium plugin, you can also find some free front-end posting plugins that may work. sorry i didn’t clarify that important detail. with frontend posting plugin all your registered members can make posts, er, questions. I’ve also connected achievements very nicely with the setup i mentioned and user stats of Q&A. I really think you could do it with MU install and a dedicated subblog to host yoru Q&A site, unless your main site is the Q&A site.
With the setup i mentioned, you can easily set up a posting form for users to start questions “with there own permalinks” since they are “posts” afterall. Questions list page is just a reworked index.php.
“user’s Q&A’s can be listed under user’s home page tab — this you can do with a plugin if your Q&A is on the main site. If on a subdomain then you can just use the author.php to list the user’s questions and answers (but answers it takes a little more tweaking)
rating system, you can use any of the top post rating plugins available. GD star plugin does good job with both “posts” and “comments/answers” <– to show best answers.
To do all you just mentioned, "registration" is going to need to be required in order to tie Question/post data to the User, with WP you can just set the comments as open to all and users will not need to be registered to answer. But IMHO I always just make everyone register quickly with just the email and name, that's what they would be entering to comment on open commenting anyway, so why not register them as a user at that point.
your thoughts are not un-realistic at all. it's doable and been done!