How to root samsung Galaxy Note 2014 edition?
Are you sure you invested enough time in searching the internet? I just found this forum and another forum after one search. To answer your other questions:


In short, you will need to use ODIN (a computer-based tool used for writing to your device while in "pre-Android" mode) to flash (a fancy phrase for installing) a custom recovery (ClockworkMod, aka CWM). That custom recovery will allow you to flash a superuser app that will handle granting root access. All files necessary can be found by resorting to the linked forums since SO can't host files.
rooting does not remove your version of Android. In most cases, it will actually wipe all of your data (factory reset), so make sure to backup anything that you need beforehand. Being rooted does leave room for flashing different versions of Android if you wish to do so in the future.
Sadly, I didn't have any luck finding Linux drivers for the Note 10.1. Windows drivers available here.