Animations and character movement

Hi all!

I’m developing a first person game with oculus rift and I’m the animator.
I tried searching the web for answers to my questions but I couldn’t find anything (maybe it’s just me not being able to search xD), so I came to ask you.

We have some quick time events in wich, after the player presses the right button, the character jumps, climbs and runs to different positions. Now my question is, as an animator, how do I accomplish that? Here are the questions in detail:

1- Root: my character has the skeleton root in 0,0,0 (using maya). When I create the animation (for example) for the character to jump from a block to another, do I have to move the root too (and eventually using Root Motion)?
2- After the animation will the character be in the new position or will he go back to his previous position? (and eventually how can I make him be in the new position?)
3- Must all the animations be with the root at 0,0,0 or can I make animation with the root where I want?

Thx all for the answers^^