Animating bow and arrow

I’m trying to create a little game where you have to shoot with an arrow and a bow (in FPS view). Though, I can’t find how to create an animation where the character is bending the bow. I mean, I have an animation for bending (which I got from Mixamo), I have a bow that I can animate so it looks like it’s being bent, but I don’t know (and don’t find) how to sync the two animations, and how to do the whole thing work together. Also, how do I do in order to have the arrow moving back when bending the bow ? Do I have to also have an animation where the arrow is just going back or can I do it in another way?

I have created a series of tutorials to cover bow and arrow mechanics. But it is now in first person mode. It is a third person character. still i think you can use the same method i have used to synchronize bow animation with the character animation. Here is the link to the playlist