Richlion, feel free to ask any question you need answered to help
Once you've got the correct cable, the notebook should work well with the external monitor, using nvidia-settings to control the nvidia driver and video card outputs. The nvidia-driver is built/packaged against each specific kernel version (you'll note the same version number on the nvidia-drivers for various kernel installs). In that way, the kernel and driver are linked.
nvidia-settings (several desktop environments can also enable an external monitor) is the nvidia provided program to control which output(s) are active, resolutions, and other parameters such as "clone desktop" or "extend desktop" to the additional monitor.
I have and use a similar laptop with same series of nvidia graphics to drive monitors, projectors (for presentations) and HDTV's to watch movies while travelling. My laptop has both a VGA and an HDMI output, both are useful, the HDMI output is digital and the one I prefer for ease of connection and cable storage in laptop bag.
I hope all the information helps, if not, ask again