How long they take to cook is dependent on how hot your wood stove is burning (flames or coals) and how thick the tortillas or pupusas are. My pupusas took about twice as long as tortillas because they're huge and stuffed thick. How thick a plain tortilla is depends on your likes and your technique. I used to live in Guatemala, where the tortillas are thicker than in Mexico, because they're used like spoons rather than wraps, so that's the style I make. They are definitely more fragile when you make them thinner, but it just takes practice.
You'll see the edges getting dry when they're ready to flip. To flip them I used a spoon. It's good to have a pot grabber since there's nothing holding the lid in place. The photo below shows my buddy demonstrating the technique, checking for done-ness.
Also, I don't see any reason why it shouldn't work on a Caldera Cone in wood stove mode. But just like when you use a big pan on a small stove burner, the hottest part is what is directly over the flame.
Good luck, and enjoy!