This is a function of the application, and frankly I do not understand why this is the standard GUI behavior for every Mac application. It should ALWAYS open into the state in which it was left. The rest of the application does, but not that. This behavior and the abysmal performance of the full screen tabbed Finder is an embarrassment to the Mac and Apple.
There is a way to make an application to open in it's own window. Open "Exposé" using keyboard (f3 on my system) or a 3 finger swipe from the top (My setup is from bottom) of trackpad. Create new "Spaces" by clicking on the "+", this creates additional space (you can create multiple spaces). Open FCP in that window. In the "Dock" Control click the icon and choose "Options>" then click on "Assign to this Desktop". Now FCP will have it's on "Space"
As to "Full Screen" and last state, Ya this could be better. You can resize the window, then quit FCP. The app is supposed to open in that size, but sometimes it loses the last size. You can try to force an app to "remember" size by moving curser to edge or corner of window and holding down the "command" key while resizing window. Now quit FCP (or other misbehaving app) and it should "remember" last state for the size of window.
I agree with Tom, this could be better.
Hope this Helps, Greg