So a Fermi Question is just another way of saying "back of the envelope calculation". These were made popular by Enrico Fermi, who was famous for doing back-of-the-envelope calculations.
So here's a website which generates Fermi problems for you.
Just refresh the page until you find a Fermi Problem which looks interesting, and then try to solve it (try to use Google as little as possible). Then tell us how far off you were, and how you managed to solve it!