In the application, what workshop / publishing experience should I include?

Any writing experience with writing, publishing, or writing programs is relevant, but just include the main achievements. Include high school achievements only if it's above and beyond the usual English classes and you don't have much else.

Should I submit fiction or nonfiction? Does it matter if it's published?

You should submit the writing sample you're genuinely the most proud of / think is the most representative of your ambition, and keep it to one piece. I don't care if they were published or not, and nonfiction and fiction are equally welcome.

Does experience level matter? would a beginning writer's sample have to be, like, the work of baby Nabokov?

I'm looking for talent and commitment—people who both demonstrate promise and plan on following through with their writing careers even after the class ends. Sometimes the track record helps me gauge seriousness. But a good manuscript takes priority over an okay manuscript regardless of background. Usually more experienced writers have stronger manuscripts, but not always. Baby Nabokov would not be admitted because he would not be drinking age.  

Is CRIT a substitute for the MFA? Is it a good preliminary step before an MFA?

Apply to CRIT if you want to take CRIT, not toward some other institutional purpose. For now a CRIT credential doesn't mean much, though neither does an MFA degree. 

Should my writing sample be close to the 3K word limit, or can I submit something shorter?

Submit your strongest work. If your strongest work is good but, like, 300 words, I might suspect it's because you don't have a lot of polished writing, and I'd probably ask to see more work. No need to hew close to 3K words, though; more words isn't necessarily better.

Do we have to workshop the writing sample we applied with?

Nope. Your workshop is your time; you can submit whatever is most useful to you. Usually it's something that you've been working on for a while, but you know it can still be improved, and you've hit a dead end with it.