How can I run an application full screen on a second screen?
Real FullScreen applications will normally run on the Primary Display and they will rarely allow you to configure that. Some applications, however, are running in a “false” full screen, and are just “maximized” applications on top of everything, including the dock and the MenuBar. Some of the latter can be moved by applications like SizeUp and similar (note the usage of the word ‘some’). 

In order to change what your primary display is, you have to go to System Preferences -> Display and the click on the “Arrangement” Tab. And then you have to click and drag the white menubar to the display you want to make primary. Take a look at the attached picture. Remember you have to click on the white square representing the Menu Bar and drag it to the other. 



The consequences of doing that is that your Dock and your Menu Bar will be moved onto the other Display.