I have just discovered my ideas about rhetorical questions were completely WRONG. Perhaps others have been under the same misconception.
* * *
I found this in The Oxford Essential Guide to Writing by Thomas S. Kane. This Guide is almost the same as an earlier work published by Oxford University Press (that was aimed at students in England). This one has been adapted to be suitable for students in America and is published there by Penguin books.
A rhetorical question is a variety of direct question and must be closed by a question mark, no matter whether the writer intends to answer it—or to receive an answer—or not. (The notion that a rhetorical question does not require an answer is inaccurate. Rhetorical questions are often asked precisely so that the writer can compose the answer. And even when the writer does not state the answer, he or she expects the reader to supply it.)
There are things that look like questions but should not have question marks. I have found these examples and explanations for those.
1. He asked if you were going downtown." That is an indirect question. It requires an answer, but it is expressed as a statement and so is closed by a period, not a query.
2. A request disguised as a question does not require a question mark. Such formulations can usually be reduced to the imperative. (For example,) 'Would you kindly respond by March 1' (could be written as) 'Please respond by March 1'.