WP Accessibility is inserting some information via javascript. Is this really accessible?
Yes. It does require that the user is operating a device that has javascript support, but that encompasses the vast majority of devices and browsers today, including screen readers.
I installed WP Accessibility and ran some tests, but I’m still getting errors WP Accessibility is supposed to correct.
Even if WP Accessibility is running correctly, not all accessibility testing tools will be aware of the fixes. Here’s a resource for more information: Mother Effing Tool Confuser. Additionally, some of these fixes depend on certain standard functions being present in your theme — particularly wp_head(). If those aren’t present, the fixes won’t work.
What exactly does WP Accessibility do for me?
That’s pretty complicated. I recommend reading the WP Accessibility page at Make WordPress/Accessibility for detailed descriptions of each feature and links to further reading.