I don't use fondant, but use RBC. I use a fondant roller with it, which is old and only came with one set of rings. I believe they are 1/4-inch. Someone correct me if I am wrong about the thickness.
Enlighten me please! 
There's a couple recipes on CC for rolled buttercream. Basically, it's a rolled icing alternative to fondant. Some complain it's a bit greasy because it's made with veg. shortening. However, others say the shiny/greasy appearance disappears if you let it set on the cookies over night.
I tried it. Liked it. But, wanted to try marshmellow fondant. I ended up using a sort of hybrid recipe between the rolled buttercream and marshmellow versions. I think it's called marshmellow rolled buttercream. It's a recipe on CC. I like it for cookies. It's pretty darn sweet but if you put it on a cut out that isn't super sweet, it's a nice balance.
I'm new to cut outs and have little patients for learning piping. Although, I am improving. The rolled icings are a nice way to get a neat appearance with out a lot of effort. 
I roll my fondant out to 1/8" thick using the rings on my rolling pin. My cookies are 1/4" thick, so it makes a nice balance.
Same as above but I am impatient with the rings and eyeball it...
Why are putting the fondant on hot cookies? I would be worried about melting fondant. I find it better to cool, brush with corn syrup and place the fondant cut- out on top. If you are getting stretching, then use a bit of tylose in the fondant or gumtex if increasing the PS doesn't work!
cakesrock - I guess the thought behind putting your fondant on right when the cookies come out of the oven is that you don't have to use a "glue". It sorta melts the fondant just a little bit & it adheres.
I've tried a bunch of ways. Piping gel, watered down corn syrup, thinned preserves, and the "hot" method. I think they all work...it's just a preference.
I think the preserves is a great idea to add flavor. But...an added cost as well.
cakesrock - I guess the thought behind putting your fondant on right when the cookies come out of the oven is that you don't have to use a "glue". It sorta melts the fondant just a little bit & it adheres.
I've tried a bunch of ways. Piping gel, watered down corn syrup, thinned preserves, and the "hot" method. I think they all work...it's just a preference.
I'll have to give it a try!
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