I am surprised by the reactions here. I did not receive that e-mail but I receive all sort of weird inquiries for my websites, (at least 2 or 3 per day).
I don't understand why people are so mad about it or even panicking.
With regard to GDPR, the "respond within x" is simply not applicable. The one month period is strictly for any requests concerning Article 15 through 22 and none of the questions are talking about any of that.
Now, if one of the questions was something along the lines of "do you process any information related to me?" then it would potentially fall under Article 15.1 and would require a timely response. IANAL, however, I think in such cases you could simply point to a privacy policy, which you are already required to have.