No. He was sinless in his human nature.
Not at all. We make a distinction between human nature and sin. It all goes back to having a proper understanding of the Incarnation.
Jesus was fully human, with a human nature like ours. But He was not subject to Original Sin, because it is contradictory, as pegleg explained above.
What we call "Original Sin" is a description of the lack of fellowship with God that resulted from Adam's Fall. Since Jesus is God, He can hardly be said to have a "lack of fellowship" with God.
Therefore, Jesus had no Original Sin.
SD