Translation:The largest apple producer in Brazil lives here.
Is there a rule for deciding the best way to parse this kind of sentence that has a "de ... de ..." structure?
In English I can imagine two sentences "The largest apple producer in Brazil lives here" (accepted and what I put) or "The largest producer of Brazilian apples lives here" which I'm not sure works.
Also, another question, does "mora == lives" work here? If they are talking about a company rather than a person there must be a better word. If they are really talking about a person then he or she must be very tall, fat or both.
"Morar" is more colloquial, used more often than "viver" (onde você mora? - moro na Alemanha.) The sentence you quoted would be "o maior produtor DE maças brasileiras (or "maça brasileira") mora/vive aqui." Now, if it was related to a company we'd probably say: "a maior empresa produtora de suco(s) de maça (apple juice) fica/é aqui" (better to use "ficar")