They're just barely in the black, if at all. Seems like I vaguely remember an AllThingsD report that they were might hit revenue positive briefly this year before they'd quickly blow it all on new hires.That implies that they're making an impressive revenue. Right now, Facebook has money to burn. If they find that they can't increase revenue, they'll be able to significantly cut back and make a profit, similar to what MySpace did recently. For now, they don't need to worry about that.
I don't know where you're getting this Facebook has no competition business. Everything on the web has competition, and Facebook is no exception.
According to Alexa, Facebook has five times the daily reach of MySpace, which is its next-closest competitor. It's got six times the reach of Twitter, which is called its competitor even though it's not. It's fifteen times larger than the number three network, which is Hi 5.
That's user interaction. Facebook also has more pictures than any other web site in existence, more than Flickr, which is the largest photo storage site in existence.
Barack Obama, who may not be the largest Facebook page, has twice the followers of APlusK on Twitter, and on Facebook he has vastly more functionality than APlusK does on Twitter: he can push nearly anything at users directly from the site, no third-party needed.
It's hard to track Note use and Video use since Facebook's based on privacy. However, I'd make a bet that Facebook's videos are enough to place it in the Top 10 for video sites worldwide. I don't know how I'd compare notes.
Google Search has competition, because it's possible to force search engine use through products. (I've used Bing a few times in the last month because I see it when I search on Facebook.) Yahoo Mail has competition, because its service has certain aspects that are unpleasant. (Email ads, for instance.) Facebook has none. In fact, because Facebook's core service is so incredibly tight, I'd bet that Facebook could upgrade nothing for two-three years, and it would still maintain its lead over competitors, solely for the reason that it can't lose that lead unless users see something elsewhere that's so compelling it makes them switch. I can't think of anything that compelling, save perhaps mobile networking, and Facebook's already the top phone-based social network despite not yet having location-based technologies.