Well, what your client is asking for is simply quizzes in Moodle and doesn't need any other app to be developed.
However, if you want/need (because of client requirements) to set up a web 'app' then look at somehting a lot simpler such as a scorm activity, Xerte or H5P to create the quizzes, or even using LTI (Learning Tools Interoperability) for passing scores back and forth between your chosen quiz and Moodle.