I can open internet links in Notepad++ by double clicking on a link. Is there a way to do this only using keyboard? I mean are there any key board short cuts to achieve this?
Officially, no. At least in Notepad++ 6.1.2
In Settings > Preferences > Misc you have only "Enable Clickable Links" - not a word about keyboard.
In Settings > Shortcut Mapper > Main Menu, Run commands or Scintilla Commands there is no reference to this.
A macro cannot be recorded with this in order to assign a shortcut to this macro.
The "Launch in..." commands send the entire file to the chosen browser.
Of course, if you'll find a suitable plugin to do just that then you're lucky. Install it and assign a shortcut to it.
...but if you're quite extreme you can enable (on Windows) Mouse Keys and use the numeric pad as a mouse, hence you'll have the "left click" on the keyboard.