Is it possible to fake a higher resolution

If you attempt to clone the laptop screen to the external monitor, you will only get 1366x766, however, if you use the external monitor as either extend or as the only monitor, you will get 1920x1080.

Please note that the laptop screen resolution should be in the specifications when you buy it - unlike CRT monitors, flat panels are made up of a set amount of pixels and whilst you can choose a lesser total and "stretch" (or letterbox), you can never go bigger than the total (excluding on a few graphics cards which allow panning - but this is rare now).

Both the Intel and Nvidia GPU seem to have a max resolution that is dependent on the connection type.

From Intel Graphics Reference and nVidia the max resolution:

• Display Port: 2560x1600
• HDMI/DVI: 1920x1080
• Analog VGA: 2048x1536

The Intel link is less clear that HDMI and DVI are less than the DisplayPort but there are a number of other sources that claim this (here, here and here).

The specs to your laptop show that it only has HDMI out which appears to be the limiting factor. You would need to have a display port out on your laptop and into your monitor to use the larger resolution.

To answer your other questions:

• Yes your max resolution will be limited by the max that the video adapters will support.
• Yes you have two adapters but the OS is supposed to dynamically handle which one is used (see here, here and here)