Definitely not "be dead"; that's very incorrect. My first instinct is to say that "died from" is very literal. You use it to very literally say something caused someone's death. Someone died from a heart attack, or died from a fall, or died from cancer. But "died of" is a little more poetic. You might say someone "died of a broken heart" or "died of fright". The person probably didn't actually and literally die, but it's an exaggeration that uses the idea of death to make a strong, emotional point.

I believe the "be dead" issue comes from the English variations of "to be" as a verb. "Be" (or "to be") changes completely depending on the rest of the sentence; in this case "be" is changed to "is," which is another "to be" verb. There are actually a few different words that change "be" depending on the subject and tense. (That means that different words do the exact same thing depending on the sentence.) It's just a matter of knowing which "to be" verb fits where. For the "of/from" question, either is correct technically from what I understand. I think they are both used in the past tense, though. "Dead from" and "dead of" both seem incorrect to me, whereas "died from" and "died of" both sound correct. Usually explaining the cause of death will be past tense, which is probably why this seems true. Hope this helps!