After being cursed by Voldemort for the second time, Harry spiritually goes to King's Cross and talks to Dumbledore. Is it like a coming back to life scene or is it caused by the dying Horcrux (or rather Voldemot's soul piece) inside him?
It's unlikely that it's caused by the "Horcrux" (remember that Harry wasn't actually a Horcrux in the first place, so I assume you meant to say "Voldemort's soul piece"), but there's no direct evidence either way. Most of what JKR says seems to point to it being a limbo state where Harry has to choose between moving on to death, and returning to life:
According to Dumbledore, it's uncertain:
“Tell me one last thing,” said Harry. “Is this real? Or has this been happening inside my head?”
Dumbledore beamed at him, and his voice sounded loud and strong in Harry’s ears even though the bright white mist was descending again, obscuring his figure.
“Of course it is happening inside your head, Harry, but why on earth should that mean that it is not real?”
“Well, where do you think we are?” asked Harry, a little defensively.
“My dear boy, I have no idea. This is, as they say, your party.”
Unknown, on purpose.
Elisabeth: In the chapter of kings cross, are they behind the veil or in some world between the real world and the veil?
J.K. Rowling: You can make up your own mind on this, but I think that Harry entered a kind of limbo between life and death.
(J.K. Rowling and the Live Chat, Bloomsbury.com, July 30, 2007 (2.00-3.00pm BST).)
Katie B: Why was kings cross the place harry went to when he died
J.K. Rowling: For many reasons. The name works rather well, and it has been established in the books as the gateway between two worlds, and Harry would associate it with moving on between two worlds (don't forget that it is Harry's image we see, not necessarily what is really there).
Unknown as of yet as that point in the timeline isn't yet on Pottermore