Generally, only living people are "celebrities". You could probably say that people can only be classed as "celebrities" when their everyday existence and activities have become of particular interest to the general public; so death, as a largely inactive state, naturally tends to diminish celebrity.
Nonetheless, celebrities may have a long twilight, after their demise: in the case of Michael Jackson, for instance, medical disputes, the interest in his will, etc., have given him a kind of artificial afterlife.
As for your question, you could rephrase it thus (note that "whom" is wrong, since the relative pronoun is the subject of "are"):
1. Does the word "celebrity" only apply to famous people who are still alive?
Not a professional ESL teacher.