That's right. "Do you like apple" would be wrong. Apples are countable, so the singular "apple" cannot occur without a determiner before it. "the apple", "an apple", "my apple", "this apple" are all fine, but not just "apple". This is true of all countable nouns.
The singular of uncountable nouns, in contrast, may occur without a determiner, as in "I like wine."
All three are correct. In every language there are often several ways of saying the same thing, and different people prefer to express themselves in different ways.