First, as I have been asked this a thousand times, is there a difference between a fiddle and a violin?

Just the words, not the instruments. Folkie fiddler types may have flatter bridges, may have more fine tuners stuck on. Classical types probably modify their instruments to suit their own preferences too

Do fiddlers use alternate tunings? I understand that the usual tuning is G-D-A-E. Why is this best?

One alternate tuning is G-D-G-D. Another I've heard of is A-D-A-E - the 4th string is just tuned up a note to be used as a drone on some tunes. (Midnight on the Water is one.)

This is just conjecture, but I think tuning the instrument in 5ths allows the most notes on one string before going onto the next. You got 4 fingers you can use, and 3 or 4 notes between one string and the next. You can play all the keys. Alternate tunings are popular in 'fiddle' music because there are a very few common keys and you can play open strings as drones.

What pitfalls lurk for the beginner? I would rather learn correctly than to have to re-learn later.

The biggest pitfall, I believe, is the bow and bow hand. Practice in front of a mirror to get the angle right. Keep your bow-hand wrist loose so you can keep the angle at 90 degrees and prepare to do those fast bow strokes. It's a bitch and a half to un-learn this, and I speak from experience.

What other questions should I be asking that I haven't even thought of yet?

Questions I wish I'd asked when I was first learning:
You think I'll learn faster if I play with someone else. Answer: unequivocal YES. Find a practice buddy or a beginners session in your area.
How do you know when to change the direction of a bow? Answer: fiddle tune books will have it marked. Sometimes it depends on the style of the tune - some styles change direction with almost ever note while others have a bunch of slurs. You can also figure it out by the sound of the tune once you get your fiddle-feet under you. You probably aren't prepared to think about this just yet, but it's something to be aware of for the future.

As to classical violinists playing fiddles, whether or not they can play fiddle tunes and sound good has little to do with what knowledge they already possess. It has to do with how well they can hear. I've heard some that were locked into the already-known style because they can't hear the differences in the way fiddle music sounds. (This can also be true of an Irish fiddler trying to play Cajun music or any other example of going from familiar to unfamiliar.) They don't listen, can't listen, or are unwilling to adapt. I've also heard classical players who joined in a tune, sight reading at speed, and managed to sound beautifully appropriate, get grace notes in and improvise a bit because they were paying attention to sound.