Samsung note 4 users pls help me out

1- this phone came with 3050 ah battery and i heard that they have its 4000 ah that can last well pls if so how do i get it or any battery that can work better than the one that came with it
2- I want to root this phone so that i can have acess to many features eg to move applications to sd card because i have try so many application to move applicationsss to sd card and is not work the only one i know it can work is links to sd application which you have to root your phone so iam confuse to root or not.
So simply i need a good and lasting battery ,and do i root my samsung or not