|You don't have to re-install the operating system if the video and the operating system works fine with an external monitor.|
I know almost nothing about any flavour of Linux.
"Is it possible to install a OS (booting from a CD) using an external monitor?"
Never plug in a monitor's video cable while the computer is running !
Some laptops will display on an external monitor without you having to do anything.
Other laptops have a key combo you must press to toggle enabling the external display only / sometimes both displays / the built in display only - see the User's or Owner's manual for your model if you get no display from an external monitor.
If you also get no video on the external monitor before the operating system attempts to load, you have the rare case where your video adapter is not working in it's default VGA mode that does not require drivers - since most laptops have a built in video adapter, in that case the only cure for that is to replace the mboard.