It was the Shimonesky Treaty that allowed Japan to have Taiwan. The San Francisco Treaty is when Japan gave Taiwan to us although Chiang Kai Shek and 2 million of his Nationalists fled there, while we were busy facing off against Stalin.
Yes. The Shimonoseki Treaty was the peace treaty for the First Sino-Japanese War in which Japan had soundly defeated China. It also granted Japan Port Arthur, but then the Triple Intervention of France, Russia, and Germany caused Japan to give Port Arthur over to the Russians, and that was a significant initial step leading to the Russo-Japanese War.