Authors of quizzes set the embed authorisation parameter of each quiz.
To know if it's allowed to integrate a specific quiz, go to the embed section, at the bottom of the quiz.
To know the identifier of your quizz and its link, click on Share.
Clic on the Facebook share button at the top of your quiz to add it in your wall.
To integrate it on a specific tab, create a new Facebook application and copy-paste the embed code in your app parameter. To finalize, make the association between your app and your page
Whether for integration in javascript, as in iframe, you can set different colors for the background, the font...
You can define these settings in your account, so that it will be applied to all your quizzes.
Then, if you want to customize a quiz among others, you can do it by clicking 'Manage my quizzes', and 'Integrate this quiz on my site or my blog'.