I am making a game where the fp player will control an axe.By doing this, would i animate the FP arms and axe in blender and or do i animate the axe separately in unity??
It depends on what your trying to do. If it is a pretty basic attack you can just animate in unity to keep things simple. For more complex animations it is more efficient to animate outside of unity.
Yeah its pretty complex, but with outside programs like blender, would i parent the axe to the hands and animate the hands and axe like that? Or separate?
Easiest way would be to parent axe to the hands. Then animate from the whole setup.
Ok that actually worked out well ahah, thanks!!
To parent the axe to the hands, how would I do so? Do I rig the axe? If so how?
Step by step process please?
Put both the axe and hands in your scene. Parent the axe to the hands and position it so it looks like the hands are holding it. Then save as a prefab and animate how you like 
What if I wanted to animate outside of unity? Like blender?
Personally I’m making a first person game myself so I have only needed one complex animation for a bow in my game. It may be different than what your doing.
What I did for that animation was imported my hands and my bow into blender and animated them together. Once done I imported them together into unity and went from there. A really good guy to check out is xenosmash on youtube. He has great tutorials blender to unity.
Thanks, he turned out to be a real great help!!!