SAMSUNG GALAXY NOTE2 TOOLKIT seems to be able to do all in a nice package.

i got a question, once i received my note 2, what are the check and test i should do to ensure the set is all right and good. i mean any app that can help me check.

Triangleaway only clean flash counter
It will not remove root
If rooted , no matter what you do you cannot have OTA update

Easiest and fastest way to update firmware for rooted phones : download the latest rom from sammobile.com/firmware
Flash the extracted tar file as PDA in PC : your root n CWM will be gone after flash
You need to root it again and have CWM installed thereafter

OR Flash the extracted tar file using Mobile Odin Pro in phone ( select keep everroot and just select wipe caches will do). PHone will remain rooted but you need to install CWM again

If you plan to keep root/CWM it is better to flash it in PC using Odin. After bootup just flash Chenglu root/CWM file in PC using Odin