Answers...
(I think I am a "Hitter" because)
My thought over the ball is to hit down using my right side, also I like to bend my right wrist back... Am I a hitter...? ( Smash that club down )
What you have is a couple of "Swing Thoughts" that work for you.
I have used similar thoughts over the years, and had students using them too.
But, really, I wouldn't call it "Hitting."
"Hitting" by definition, is Force Across the Shaft. Think of pushing a shopping cart. You are putting force across the handle bar.
The MATH says you won't hit it anywhere using Force Across the Shaft only.
To achieve any kind of good clubhead speed, you need LOTS of Force
Along the Shaft, what some (not me) call "Swinging."
A good way to picture Force Along the Shaft is pulling on a rope to ring a heavy bell. Heavy enough that you had to use your whole body to pull.
Maybe you have plenty Force Along the Shaft, and using a Force Across the Shaft thought helps you balance it out.
The OPTIMUM usage of the two different forces is this:
You pull from the top, and when the club is vertical for the last time before impact, you add pushing.
You apparently, have tapped into this.
Plus, keeping your right wrist bend back, along with the MASH IT DOWN with your right side thought, probably gets your clubhead path into the ball more direct. Which, it seems like, is a good thing for you.
I wouldn't add float loading to these thoughts unless you needed more feel or ummmph.