1) Yes it is correct. Each version of that sentence is grammatically correct, but they all have separate meanings in English. The first sentence, "He already knows the story" feels as if it is being used at this exact moment, being told to someone. You are using "knows" because something is currently related to the situation, such as someone about to tell a story that he already knew. "He already knew the story" is more in the past, as well as "He had already known the story". I am trying to think of a better way to separate the last two, but being as I am tired, I can't think of a good answer.
2) Yes it is
3) The structure is correct, but it is worded in a way that sounds slightly awkward. It would be more natural to say, "Is this statement correct?"