My experience from asking questions by email is that friendly, short and clear questions are usually answered in a similar way. Once, a friend from the Studienstiftung whose way to ask is more formal, like the descriptions above, and I made an experiment: The short and less formal mails work much better. Status etc. are the more irrelevant the brighter the receiver is, good brains obviously are good communicators too. Of course I try not to ask questions which sound to me as if they could be an exercise or answerable by a web- resp. library search. Occasionally, some people are a bit mad and, when asked by a stranger, suspect conspiracies by competitors under a pseudonym, or get an ego problem if noticing that their articles are readable even by non-specialists, but such cases are much rarer among mathematicians than among e.g. philologists. Conc. "If you receive a response and the professor signs with their first name": If it's a professor in England, don't refer to him by his first name in your next mail. If it's a professor in the US, you can switch to the first name.
Edit (on the comment below): It would be great if sociologists do some email-experiments on that. My experience is that mathematicians are far better and quicker in answering email-requests from "outsiders" (e.g. I never use a university-email account) and among mathematicians, the more known one's reactions often are faster and more extensive than that of others, despite they probably receive a lot of such mails. Even when the request was about some outdated issue, one often receives links, texts and suggestions directing to (in their view) more interesting, open, in any case very stimulating themes. However, "communicative skills" exist in different ways, e.g. here a mathematician's collection of personality tests, who thinks that email-communication fits well to the specifics of high functioning autism, which probably is overrepresented among mathematicians.