How can I ask a professor for time-sensitive information when they are out for a family emergency?
I'm an academic who has had to cancel class and office hours due to emergencies myself. We are all pretty tied to email these days wherever we happen to be, and regardless of what is going on in our personal lives, our professional responsibilities to continue to limp along. Depending on the specific nature of the emergency and the demands on their time, the professor may actually be able to help you nevertheless, but i) may well need reminding, and ii) may have higher priorities at this time.

I would send an email like the following (and if I received it, would respond as positively as I am able if the tone does not rub me the wrong way.)


  Dear Professor X:
  
  I understand you have had a family emergency. Sorry to bother you at
  such a time, and I fully understand if you are therefore unable to
  respond to this email. However, in case you happen to be working
  remotely, I would much appreciate your comments on the below, since I
  need to ... by .....  Or is there someone else you would recommend I
  contact instead given the timeline?
  
  Thanks and apologies, ...