The recommended method is flashing the rom with the file "flash-all.bat" or you can use Nexus root toolkit which do for you all the job. Because you are in kitkat, you must wipe your device because their are users who says they have a lot of bugs. After you flash the rom you can use nexus root toolkit to flash root and costum recovery.
For original kernel you need to find kernel same as the original but can rooted. That because in android marshmallow you need a coustm kernel for root, Google blocked the way of root device with their kernel.
Hope I helped