What accounts for the pitch of a man’s voice (or vocal range), his testosterone level or the actual shape of his vocal folds (cords)? And when a man’s testosterone level drops, from age or other factors, does his voice get higher . . . or is his range set at puberty?
Voice is determined by the shape of the vocal cords, and shape of the vocal cords is determined by testosterone. The shape might change a little if the testosterone is taken away, but the only way to get a castrato singer is to snip before the change. Certainly, there’s nothing to the old gag of someone getting kicked in the crotch and immediately talking soprano.
So if I have a fairly deep voice, does that mean that I’m producing more testosterone than average?
I have been known to be awfully manly 
Thinking of the scene in Crocodile Dundee…
It means your vocal cords are thicker than normal. Whether that’s due to abuse of them, normal (for you) development, or hormone imbalance - that’s why there are lab tests.
Possibly. You could also be talking in the lower end of your range. Have you ever run into someone who talked like Bette Davis and sang like Kristin Chenoweth? I have.
“I call you on the telephone, my voice too rough from cigarettes.”
I know someone who speaks with a low, husky voice, yet sings high tenor. And yes, he smokes.