Hello. Being able to do a quiz from within the Moodle mobile app is something the mobile developers are working on and hope to have it ready soon - but at the moment, you have to do a quiz from the website.
We've had success writing the quizzes using Captivate and creating scorm packages rather than Moodle quizzes.
This works for the limited question set in captivate as the scorm package does all the work and just returns the result.
It's a workaround until the developers have a chance to crack the much larger problem of native Moodle quizzes.
That will be a very welcome addition.
I hope that they will fix the 'app to full site' SSO eventually too, so any contributed plugins will just work on mobile in full site mode. Without having to login again.