I have a default install of the full Q&A plug-in on my local machine. For questions that I've already created, I'm not able to update/edit/add any new tags or the category. I can go in and edit a question, and the Title and Question will update. However, if I change the category, or attempt to add any new tags, they're not added.
I tried to recreate on your demo site, but I'm not able to create an account to create/edit questions.