@Robo: That shouldn’t be a problem as the Catch Box Free Version and Catch Box Pro version uses the same code base. Just has lot of feature added. So, that shouldn’t be a problem.
If you are using Custom Menu from “Appearance => Menu” and Custom Background from “Appearance => Background”. Then yes, for these you need to reassign it. This is default WordPress functions and if you change to any theme you need to reassign it.
For menu, just go to Appearance => Menu and then select your menu in the header and all other section as per you need.
For Background, you can get the same image or background color from Appearance => Background and then select color or chose image from your media library.
I hope this will be fine. If you have any problem then let me know then I will contact you and do that for you.