I just used other people's a few times. No expert in construction! The one in new zealand was very DIY low tech - a street sign was bent to create the inner wall of the oven, and
cob was piled in layers around that (so I was told - didn't help with the construction). And it worked great!
I have a book about bread oven construction, and though it recommends firebricks and
concrete as the building materials, it covers some basic principles for oven design that seem to be important - it would
answer all your questions about chimneys, for instance. The curve of the dome, for instance, can vary according to the cultural slant of the creator, or purpose of the oven. Pizza ovens have a flatter, longer shape, while "true" bread ovens are more of a half-sphere, seems to me. I'd want one that was all-purpose. Anyway, the book is called
The Bread Builders, and I'd recommend it. The first half is all about
sourdough bread, the second about the ovens.
So far as I can tell, the goal with an earth oven is a really hot fire, and really hot fires don't make a lot of smoke. There might be a bit right as you're getting the thing warmed up, but it shouldn't be smoking the whole time you're cooking. The coals of this big hot fire are pushed back to the perimeter of the oven chamber right before you put the food in, and the residual heat of the whole mass of the oven (as well as air-current stuff created by the dome - too complex for me to comprehend) is what creates the amazing cooking environment.