You are addressing this to the maintainers of Moodle.
Can I ask, what is your role? Are you someone who regularly uses Jaws to access the web, or are you a non-expert user of Jaws, for example a software developer or tester, who is trying to understand how well Moodle works? If that latter, you need to realise that Jaws is a powerful bit of software that you probably don't know how to use well, and so it is easy to have it in the wrong mode for effectively accessing a particular page, or something like that.
Unfortunately, the other thing to realise is that, things change with time, so even if things worked nicely a few years ago (which they did, we got some expert testing done) the web browser, and Jaws, change and there is no guarantee that things still work well, so more testing is welcome.
Anyway, your first issue probably comes from having Jaws in the wrong mode. A page of a quiz is not really a form. It is more like a page of content.
The second issue: well it certainly used to work properly in the past. If you answered one question, then when the page re-loaded, focus would be on the question you just changed.