Hello Future Tribe Mate,
My rabbi did not provide me with any questions from which to start my essay for the beit din. He left it open ended, and wanted it to come from us: what WE thought was important for them to know about us as future Jews and our Jewish journeys. In some ways I wish he had provided questions for us to answer because it would have been easier to start with something.
But, from nothing came 17 or so pages, double-spaced, of an essay that I presented to my beit din.
I think what would matter most to me were I a member of a beit din is that you were authentic to yourself. Some people are funny. If you are, inject some humor. Some people are verbose. If you are, feel free to take as long as you need to answer a question. If you are naturally concise, there is no reason that your essay shouldn't include brief answers that can be used as a jumping off point for the discussion with the beit din.
I think another thing that I would want to stress to people coming before "my court" would be that they shouldn't feel pressured to answer in specific ways: there (barring a few extreme cases like believing in Jesus as Christ or feeling coerced into doing this for your future spouse's sake) aren't right or wrong answers. If you don't know how to answer a question yet, be honest. Share your struggle; you are wherever you're at in your Jewish journey and that's okay.
But I think that the most important thing I'd want them to know is that this is NOT a final exam; nope, it's just the beginning. This is like getting your driver's license - now you get to go so many places and it's so exciting to see where you will take yourself.
If I had to guess about what information your rabbi was seeking with these questions, I'd say:
1 - What was your religious background prior to Judaism? How did you first learn about Judaism?
2 - What ideas about how to live life, what life's all about, and our purpose in life and society did you read about and have light bulb, "aha!" moments with? What rituals do you love, even if you yourself don't do them?
3 - If I were to follow you around for a week or month, how would I know you're Jewish? What Jewish things do you do, or what things do you do Jewishly on a regular basis? If I were to follow you around for the same period of time next year, five years from now, and ten years from now, what new things would you hope for me to see you doing?
4 - How do you feel telling your family, friends, coworkers, and neighbors that you're Jewish? How did/do you integrate yourself into your community? What Jewish people do you interact with and how? How do you feel about Israel, about France/UK/Argentina/FSU and other areas with lots of Jews?
5 - What subject do you want to learn more about? Where will you turn when you want to know more? What are formal and informal ways of learning?