You can add the new box above or below the existing one. I only add below if the existing box is a little low in numbers, and not particularly full, but I am going to be away from the apiary for a couple of weeks. If the existing box is strong, it is much easier to add it on top.
I wouldn’t. The less you move frames around, the better for the bees. When you move stuff, it is like somebody coming into your house and changing the position of the kitchen and bedrooms, etc. Very disruptive!
I don’t know what kind of entrance reducer you have, so it is hard to say. If the bees are really crowded, trying to get into the hive, they probably need a bigger entrance. My hives are currently 3 boxes tall (2 brood deeps and a super), and the entrance is about 6 inches (15cm) wide. I never have it bigger than that, as good quality bee research has shown that to be the size that bees prefer when given a choice. My bees are perfectly happy with that size, and it means that they have less trouble defending the hive from pests and robbers.