I probably need to flutter kick between the scissors
100 percent yes. Whether you are in cammies or not, if you aren’t kicking you are not doing it right. Once you wear fins this will help also because you can only flutter kick with fins. Do not scissor kick with fins.
I've never rotated during the stroke though, I always stayed on my side, even during the streamline
Some people don’t like the corkscrew. When swimming, consider the concept of “swimming down hill”. It important to always try and swim downhill and tuck your chin so that your body stays horizontal and your hips stay on top of the water. I prefer the corkscrew because feel like it helps me keep my hips up and swim “downhill.”
Do you feel like a top arm over hand recovery is beneficial to this stroke?
I don’t know if your instructors will care, but we had to focus staying splashless and stealthy in the water. I do think the over top recovery stroke is the best thing to do. It’s better when your hand comes all the way out of the water, however we would get scolded if we let our hand come out of the water because it splashes and is more obvious to the enemy.