No, when I press F3 for example it just shows the chrome windows, not the documents, so I don't understand.
It will depend on the settings System Preferences for both Mission Control & the Keyboard and the keyboard that you are using.
If you use Apple's wired external keyboard* or the built-in keyboard of a rMBP, then the F3 key by default is set to go into Mission Control. This is because by default the function keys are set to operate as special keys and only operate as an actual function key if you press the "fn" key (just to the right of the "delete" key on the wired keyboard or in the lower left corner of a rMBP keyboard). You can switch operation by going into the Keyboard settings in System Preferences under the Keyboard tab. You will see a check box labeled "Use all F1, F2, etc. keys as standard function keys". If that box is checked, then the function keys will act as actual function keys.
If using an Apple wired keyboard or the built-in keyboard of a rMBP with the function keys set to act as function keys OR using a non-Apple keyboard, then you can go into the Mission Control settings in System Preferences to pick which function keys will do what function for Mission Control.
* It might be true for the Apple wireless Bluetooth keyboard, but I don't have one so I am not sure...I use a wired keyboard.
I can see the menu bar so I assume they're not in fullscreen mode either.
Do you see the menu bar all the time or does it only appears when moving the mouse key to the top of screen?
If it is the former, then I might need to see a video screen capture of what is happening. I say this because the "sliding off screen" that you described would seem to describe a program/window that is in full screen mode and then you switch to another application (in this case Finder).
I don't remember this problem with windows. I remember you could get a program that would keep the window you wanted on top too.
You should be able to do this. In "normal" mode (aka NOT fullscreen mode), a Mac will operate very similar to a Windows computer. Frankly, that is how I tend to operate my Mac 99.999999999% of the time...i.e. I hardly ever use full screen mode...today is one of the few time I have a full screen window...I currently have a Safari window in full screen mode running my TiVo online account watching the Michigan football game while I am on the computer.
Edited by smax013, 10 September 2016 - 11:44 AM.