I want to make a mango mousse cake but my springform pan is not tall enough.I saw there was something called a "cake collar" made from parchment paper. I only need the mousse part taller. Do I wrap parchment after the cake bottom layer is baked or should I put it in before baking the bottom layer? How do I keep the parchment from falling down if I place it before baking cake bottom? It makes it difficult to pour batter when nothing is holding the collar in place.

I would definitely put the parchment paper "collar" in place before added the cake batter.  I use dabs of shortening on the sides of the pan to hold the parchment paper in place and at the seam where the ends of the parchment paper overlap.