I got this right from the main source, google!! ......
Using an external monitor or projector
To project your Chromebook's screen on an external monitor or via a projector, connect the device to your Chromebook. Consult the help information provided by your Chromebook manufacturer to determine what type of connector you should use. Once connected, the device will be automatically detected and your screen will be projected, using the best possible resolution.
If you've connected an external monitor, the screen will only appear on the external monitor. Currently, it's not possible to set up an extended display. If you've connected a projector, the screen will be displayed on both your Chromebook and via the projector.
I don't have the answer your looking for but I have a feeling that Skype on Chromebook MIGHT be limited but I really want to see a review for Skype on ChromeBook to see what functions don't/still remain on the Skype chromebook app