Judit,
I'm certainly no expert at cob oven building, but I can give you a bit of feedback pertinent to your questions. If I were to build mine again, I would probably build it with a chimney. I first decided not to build it with a chimney because I wanted to keep it simpler on my first attempt. Overall, I have really had satisfactory burns in the oven. It does smoke in the beginning of the burn, but mine almost always clears as the fire gets hotter and hotter. It is typical to have the flames licking out of the front of the oven when it is burning really well, even when all the wood is pushed to the very back of the chamber. Having said that, I think I could get a much more efficient and more steadily hot fire with a chimney (as in the double chamber design). I am planning to retrofit a chimney into mine at some point for this very reason. Because I made mine slightly thicker than expected, I find that I have to fire the oven for much longer to heat it all the way through (c. 3.5 hrs). I'd like to make better use of my fuel by implementing some of the rocket stove techniques as with the double chambered oven.
About the door...I don't ever use one when I bake pizzas, as I like to have a live fire around the periphery of the oven. Yet, when I bake or cook other things like breads, casseroles, soups, roasts, etc., I think, the thicker the door, the better! In fact, though my door is not cob, a door of cob would probably by the most efficient in terms of holding in the heat during baking. My door is adequate (1.5" thick kiln dried hardwood with a sheet of tin spaced about 1" off of the inside of the door), but I sometimes find myself stuffing bricks into the door space in addition to it so as to preserve more heat.
Here's a link to a blog post about our oven if you're interested:
http://www.theyrenotourgoats.com/homestead/making-our-cob-oven/
I hope yours turns out well! It will be a valuable experience however it turns out.