"Midas" is the subject. "could turn" is the verb.
"What does that have to do with anything?" Is a complete sentence, in this interrogative sentence "that' is the subject, "have to do" would act as the verb and "anything" would be the object. "What does that have anything to do with" is an incomplete sentence, this is noticeable is you follow the format subject + verb + object. The two vary slightly in meaning. The word "anything" should not be used in the second one. In meaning, the first sentence is global and suggests that the asker does not understand the connection with "any" subject, much less the one being discussed. In short, the speaker is saying that a comment was completely irrelevant. In the second sentence, there is a subject or event being discussed, e.g. "What does that have anything to do with bowling?" The speaker does not see any connection between a comment and the specific subject. For example, someone may have commented that he could not go bowling because he was concerned about the environment.
A sentence missing a subject or a verb is a fragment.
It could be.
The story is a myth, since there is no evidence that any human has been able to turn things into gold in the way that Midas was supposed to. The story illustrates that money or riches do not on their own bring happiness.
It could potentially be the subject of a sentence, if that is what you mean.
By adding the appropriate subject-auxiliary inversion, the sentence could be rewritten as an interrogative sentence.
he had a Midas touch so he could touch every thing gold
The essential parts of a sentence are the subject and the predicate. The subject of a sentence refers to who or what the sentence is about. The predicate is the verb that shows an action. For example, in the sentence 'Bob sneezed.', the subject is Bob and the predicate is sneezed.
Able to do anything
he was subject to an investigation
Subject personal pronouns are I, he, she, it, we, you, and they.
King Midas could turn what he touched to gold.