Hi Ray,
This feature is designed for quick, informal quizzing only - all data generated is stored on a temporary basis.
I've tried all of the question types we use at The Open University and they all worked welll - although on a practical level you wouldn't use Essay, and you have to think about the width of certain qtypes (Drag and Drop onto an image might be an issue depending on where you try to embed it).
The default question behaviour is Interactive with Multiple Tries.
I've just finished writing a blog post about the feature (which has more screenshots) here:
https://medium.com/@GoTeamOU/embeddable-moodle-quiz-questions-d76b7e2cace9