In general, my reaction to "facebook will steal ur contentttt!" tends towards "No, their business practices aren't that ill-advised." However, I don't have visual intellectual property that I'm concerned about facebook using for profit. So with the enormous caveat that I don't have any skin in the game (or experience with the game), I'd be more concerned about plagiarists stealing images to sell on cafepress-and-similar-more-sophisticated-operations. But then again, every time an artist posts a link to a "high quality" image of their Derby entry, I want to scream TAKE IT DOWN!, and obviously the artist believes the benefit outweighs the risk, so I might be too paranoid on this.
In terms of benefiting from having an artist facebook page, I suspect the benefits might be concentrated in two ways: if you post links to your Derby entries and that post shows up on your followers' news feed, you might benefit from some "targeted" votes: people who are only interested in seeing your designs in the Derby, so more likely to vote for you while possibly being less likely to browse the Derby and vote for your competitors. It might also be a "home base" for your work that could drive people who see your shirts on other sites to your woot catalog, and drive your woot fan to another site if you have a print elsewhere.
Rasabi makes some great points about the complications of facebook, especially how difficult it is to get posts to show up on users' news feeds. (Are they still called "news feeds"?) It sounds like the key to showing up on news feeds is to drive people to view your page as often as possible, so more frequent posting, as long as it's relevant, may help.
Posting in ways that inspire people to post back, not just click "like," might increase a sense of community. People feel good when they feel like they're part of something; that inspires loyalty. Find a way to make your fans feel like they matter to you or their actions make a difference for you, such as by voting for your Derby designs whether or not they actually want one. ("I like KittyBunnyFooFoo! If I vote for this design, she might win the Derby! And if she wins the Derby, she'll get paid! And that will make me happy because I like KittyBunnyFooFoo!" Of course, almost no one consciously works through that thought process, so you can't just tell people to vote for you because you need the money; you want to inspire the kind of loyalty that results in the conscious thought process of "I like KittyBunnyFooFoo! *click*.")
Develop a consistent professional persona. Be gracious. Be succinct. Be humble and appreciative. Be self-aware of your motivation and goal for every post and comment. Be clear and straightforward with your word choice and syntax. Appear genuine and authentic so that people feel like they know you, but don't confuse yourself with your professional persona. Bonus points for funny, especially a sense of humor that appears consistent with that in your art. Humor is humanizing and people perceive that an individual's sense of humor yields insight into their authentic nature - but remember, this isn't necessarily your sense of humor, but that of your professional persona.
ETA: wow, this post is long! My apologies - and a huge caveat that although I've developed a serious interest in consumer psychology (which is different than marketing) and would love move in that direction professionally, my post is based on my observations of what works and what doesn't, and my own analyses of why based on what I actually do, which is essentially to figure out people's unconscious thought processes and help them modify those processes.