For some of the other probability questions, my answer is "I don't have enough information to come up with a good estimate, and I also don't have enough information to come up with a probability that takes into account my inability to come up with a good estimate". Again, I put 0.

Um, nothing complicated is required here. Consult your gut feeling and put whatever number comes up. Turning this into an actual probability is why we have calibration questions. Putting 0 is definitely a wrong way of refusing to answer the question (you can already leave the box blank, if you really want, and thereby avoid polluting other results).

As an aside, given we had at least three people with such strange interpretations of the MWI question so far, perhaps the survey should include a question asking one's opinion on map-vs-territory...

Also, after the test, I'm starting to get worried how you anonymize the questions. Releasing the data without a name attached is not anonymization, if the answers people give are enough to identify them.

I believe that effective anonymization (apart from removing names) is in general impossible. Although, for specific analyses a reduced dataset can be effective, such as all pairwise joint histograms, which I think preserves a certain amount of anonymity depending how unique each person's answers are.