1. Are all of a gaited donkey's gaits smooth, or just their running walk/rack/whatever that donkey does?

Not sure , i've never ridden a gaited donkey. I just know they exist.
2. Are there any good books or web tutorials out there on donkey conformation?

Not really , just look at it like you would a horse , same concepts usually apply. The only real difference is that they have no defined wither , it rests down between there shoulder blades.

3. Okay, saddle fit is not easy, I got that part. Is anything else different about riding and handling a donkey?

Browbands on most bridles are to tight , but thats easily fixable. If you are riding western the saddles are harder to fit to a donkey/mule then an english saddle

4. You knew this was coming. Is there any truth to the stubborn stereotype (not counting studs, I know enough not to get one of those)? Is there any reason a beginner like myself should really start with a horse as their first equine instead of a donkey?

No truth to it. They are a bit brighter then horses , they think along the lines of "will this be good for me" they are much more self serving then horses. What it comes down to is are you going to be patient enough to deal with them when they "try" you..

5. Would a mule be a better choice? Why or why not?

Its mostly personal preference. I would honestly say yes get a mule first. They are a little easier to train an finding a gaited mule is pretty easy.

6. How hilarious would the dirty looks be if I tried to board one at the big show barn my son rides at?

I would do it just for the dirty looks.