Can I use a wooden chess set for tournament?

Or one where all the pieces are rubber ducks: http://www.amazon.com/Rubber-Ducks-Duck-Chess-Game/dp/B006QMHC0C

Only if you are Black and the TD approves. Otherwise, no.

However, since Caleb is a considerate fellow concerned about even making a faux pas with a wood set, I doubt he'd force a set on his opponent even as Black.

USCF gives the arbiter/Tournament Director the final say on whether a set is standard.

A TD may state that an ornate set is standard enough to play on, but if another more standard set is available in future rounds that should be used instead. 

Or ice. They actually sell em where you make your own pieces from the molds they send. I guess you put food coloring in blacks.

I bring a $1000 set every time I play at tournaments. My opponents will usually act more professionally too. Great time all around.

Sure

Yep

I have a Dubrovnik 2 set in white and brown, with a white and brown notated mousepad board that looks like it has wood grain. Think that is okay for tournaments?

It all depends on the tournament and the director. In elite events, the sets are provided and they are all uniform.

I once played in a tournament where I used a nice wooden Staunton set. My opponent complained because the stain on the “Black” pieces wasn’t uniformly dark. The variation was minuscule, but the TD upheld his claim since there was a plastic set available and he rightly guessed that I would be easier to work with than my notoriously disputatious opponent. 

The TD  has the final say, no matter how beautiful or expensive the set is.