Stop app opening in full screen?

Without knowing what app it is, it's difficult to help you.

But you could try trashing all the preferences file for the app.
You should check for an update for the app.
Double check the preference settings for the app.

 

Can you clarify what you mean by this? Do you mean the Desktop folder, or the Desktop in the sense of the entire display of the monitor, minus the menu bar?

Again, knowing what the app is might help.