Both of these issues tend to show up when leaving an overlay(?) screen such as shiritoti for the study buttons, or the dictionary for the quizzes. Both can be fixed by force closing the app then relaunching it.
When the study buttons have the issue, their color will change when tapped, but quizzes don't start. When the quiz words become undraggable, they can still be tapped into place.
Thanks for the info - when you say overlay, are you referring to the rules that pop up when you are about to start a round of Shiritori cat, or something else? If you can shoot me a screenshot, that'd be great.
Also, when you say "study buttons" - can you tell me exactly which button(s) you are using, and on which page they are on? (alternately, a screenshot of these would also work).
I'm not sure what I meant by overlay -- I think I just had some weird assumption about how the ui functions. But coming off of shiritori cat (maybe not normal shiritori?) is when the home page study buttons are likely to be blocked. When the issue is present, the buttons will darken while tapped, but nothing will happen.