When launching a game or full-screen app, if another app is moving to a different location, this post will help you resolve it. Most games launch in full screen for the experience.

Drag the application to the right or left edge of the screen, depending on your monitor configuration. You should start to see the edge of the application appear in your second monitor.

This article explains how to move apps from the App Library to the home screen on your iPhone, including how to find an app with Spotlight and then add it to your home screen.