(1) Just as in plain 'food', both forms are possible, depending on whether the speaker is considering the nutritive substance in general, or as several discrete types. It is often in the industry or in nutritional discussions that we speak of the different natural/health foods-- muesli, royal jelly, or whatever-- and their relative merits. In more general conversation, we would be satisfied to say that we abhor health food, and love junk food.

(2) In re islands, I would think it depends primarily on the correct name of the island in question: Long Island could certainly not be the island of Long, and 'island of Long Island' is redundant. If the place does not have 'island' in the name, like Malta or Java, then I think that 'island of Java' (note lower case 'i') would be appropriate, so as not to confuse it with an improper proper name: Pitcairn Island; island of Singapore. There may be other opinions.