<<Disclaimer: Verify this information before applying it to your situation.>>

Several years ago Sully's Living Without featured a recipe for crepes, using potato starch instead of regular flour.  It works fine for me. 
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The best I've had were made with potato starch.  They're from Rebecca Reilly's Gluten-Free Baking book.  You can Google crepe recipes with potato starch as well.  There are a number on the internet.
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Haven't made them without any flour, but I've made them with potato starch (Passover) and I know you can use other g.f. substitute blends.
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Yes but not the kind that you are describing.  The kind that I have made uses GF flour.
I always have trouble with the first one of a batch.  I have thought that perhaps the pan was not hot enough and waited longer.  That did not work, then I thought the pan was too hot, it still did not work for the first one. Now I make one very small and plan on tossing it out.
The ones you are decribing sound more like a thin omlet, probably without the salt
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Someone posted a flourless (cornstarch) crepe recipe that my daughter and I made together. It turned out great! I filled some with steamed shrimp with pesto sauce and some with cream cheese filling and fruit. Try a search of the archives.
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I LOOKED AT THE WEBSITE AND FOUND THE RECIPE
http://www.foodnetwork.com/food/recipes/recipe/0,,FOOD_9936_29524,00.html
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Yes, I have, and I use them for a GF lasagna noodle.  Just swirl in a pan, then cool and cut into strips.  Use just like you would a lasagna noodle.  Delicious
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 I make a "chinese pancake" for moo shu that is basically a crepe.  The only thing that makes it the chinese pancake is the spice. When I want to alter it to be a wrap for sandwiches I change that.  
 
So chinese pancake it's sesame oil, ginger and scallions.  Sandwich wrap, it might be basil, thyme and olive oil etc...  It could easily be a breakfast crepe filled with fruit and covered in powdered sugar.  You would just need to adapt the spice.  Perhaps just a tiny bit of sugar, some cinnamon or almond extract etc. 
 
I got the recipe from glutenfreeda.com.(Under chinese pancake)  I use carol fensters flour mix for it.  I whip it up all the time in the blender and just make a few crepes to use for all kinds of purposes.  I make them extra crispy if I am using them as a sandwich wrap, and a bit thick.  Otherwise they get soggy.  
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