Does anyone put parchment or wax paper under their fondant when cutting with the cricut cake? Is it ok to do that will it cut through the paper?

Why would you want to put parchment paper under your fondant? In theory, that would make it move around while it's cutting and you want the fondant to stick to the mat. All you really need to do is lightly grease the mat and put your fondant on it.

I just figured that I would put shortening on the mat to stick the parchment paper on then put shortening on the parchment paper and put the fondant on. I figured it would be a lot easier to take the figures off.

they actually come off really easy with just a light coating of shortening on the mat. I haven't had a problem with anything sticking to the mat.

Ditto! They come off really easy with just shortening.