Can I make grain-free noodle/ravioli/dumpling dough? I'm celiac and I'm intolerant to virtually all the grains (also to corn/maiz). So, the question is if I can make noodle/dumpling dough without grains?

Yuca and potato starch are good for me, also chickpea and other legumes are fine. Any suggestions?
You could look into cellophane noodles. They're made from starch (often yam or potato), so it sounds like they'd work for you.

If you have a decent Asian grocery store around, you may well be able to just buy them, too. You'll just have to be careful to check the ingredients, as they are sometimes made with corn starch too. (I'm not sure if it's whole corn or even the starch that you can't have.)