From Converse's questions, it seems he was doing some kind of thought experiment (or perhaps a real, physical experiment) involving measuring the potential — the voltage — using an electroscope. He seems to have asked whether it was necessary to have charge permeating the space between an electroscope and the Earth when measuring such potentials. It's not clear that he was asking about relativity per se. [The 18 Biggest Unsolved Mysteries in Physics]
In the 10 questions, readers get a clue as to what Converse was asking at Numbers 5 and 6: "Would your explanation hold true for an Earth without an atmosphere if the surface of such Earth had a negative charge of considerable density?" (Einstein said yes), and "Would the potential at height h be a so-called 'space charge,' or would we have to call it some other name such as 'true space charge?'"
Einstein answered that there's no need for a charge to be in the space outside the Earth in order for a potential difference (or voltage) to exist between a point on the surface and one above.
In Question 7, Converse asked if his experiment would get the same result if the Earth had no atmosphere, and in Number 8, he asked what the density of Earth's surface charge would have to be to balance any portion of the atmosphere, "condenser fashion." Here, Einstein wrote a question mark and what appears to be the equation for the total charge of a sphere in terms of charge density.
The last question described an experiment with an electroscope, and Einstein glossed over it with the note saying, "not clear." Einstein then crossed out the typed part, which said the charge on the electroscope increases with h (height).
Original article on Live Science.