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Good question. Yes, each inhabited island (Java, Madura, Bali, Lombok, Sumatra, Kalimantan/Borneo, Sulawesi/Celebes, Papua) has their own language, at least one, they possibly have more than one languages. Bahasa Indonesia is the lingua franca (I am not sure can I use this term in this case), Indonesian people who live in different island/place with different race can communicate each other with Bahasa Indonesia. Still, people who live in remote area sometimes can't speak Bahasa Indonesia. You will know that if you watch a tv programme that visit the remote island to expose their traditional way of living and culture.
About the race, yes we are very diverse in race. E.g in Java, there are Sundanese, Javanese and Maduranese (someone can add another race if you know more). also in Sumatra, we can find many races.