I'm sure a lot of other guys can jump in with more specific info, but based on some average riding I get around 14 miles per gallon on my 07 f8, and a guy I rode with that had 07 1000 seemed to put about the same amount of gas in everytime I did so I'd put it in that range.
As far as problems, can't give you details, but seems like a lot of people say the 1000 had a lot of different issues. I had a dealer tell me recently to stay away from one while looking in the used market. Not good news to you if you just picked one up, but hopefully you'll have good luck with it.