Reminds me of Panoptic by the EFF: https://panopticlick.eff.org/
Everyone's ID would change as time passed (if they move, if they age, if they get a sex change, etc).
The best questions for this are inherently "irrelevant", since "relevant" questions tend to be statistically linked. So, questions like "Was the second letter of your first girlfriend's middle name between A and M?" is better than "Were you younger than 20 when you had your first girlfriend?", since we can likely guess the latter based on the other statistics.
It's very unlikely every ID will be unique if only asking 33 yes/no questions. I mean, look at two twins living together -- very few questions will be able to differentiate between them.
I think it's possible to do based on a random snapshot in time, however less possible if it's meant to last a lifetime.
I also think the questions exist, but not in a manner that we'd be able to come up with on our own. As in, I believe that a program that knew every detail about every human could create 33 yes/no questions that differentiated people, however I don't believe we could do it ourselves.
I also wonder how many questions would be required to ask non-yes/no questions and get a completely unique ID for everyone. For example, questions like "weight? languages spoken? birth place?".