You can use a hand mixer or a regular beater attachment on a stand mixer if you need to, but it will take a lot longer with a hand mixer.
Sour cream adds moisture, as the cake can sometimes feel a bit dry. Vanilla extract is to taste and adds extra flavor. The cake is good with or without it. If I am making cupcakes, I sprinkle the apples on top of the batter.
For the optional brown sugar glaze, smash 1/2 cup of softened butter with a silicone spatula into the baking pan, smearing it evenly over the bottom and up the sides. Crumble 1 cup of brown sugar evenly over the butter and sprinkle with cinnamon to taste.