Can I decide the order in which collections and collection groups appear in my image bank?

Yes, you can have a hero collection at the top of the page and underneath the hero are the featured collections. 

Below these are group collections and then collections that aren't promoted nor in a group. 

Here you can read more about how you promote your collections within your image bank: https://www.pickit.com/help/how-do-i-make-a-collection-a-hero-or-featured-collection