Not sure on the stacking of the cake, that talent is still beyond me as far as those types of cakes go, but I imagine gumpaste rolled thinly, is all the tissue is...
Need help creating this cake and have no idea hoe to stack it so it doesn't fall and I need to know how to make tissue paper our of fondant.
The tissue is just thinly rolled fondant or GP gathered up. You could stack this cake using styrofoam wedges, but the easiest and safest is to use a stand like this one:
I'm sure the peson who did that used the wedge method. Check out the link in my signature and it will lead you to a bunch of tutorials. Look for topsy turvy and click the one from sugar ed.
As for the tissue, just roll out gumpaste very thinly or you can use petal paste which can be rolled super thin.
I love the design of that cake. It's so cute! A square, a round, and a pillow. =o)