There is a good chance that your name is "flagged" in all of the government computers. They will probably tell you have a seat and wait for your ID, then... Surprise--you are under arrest.
You really need to find a local lawyer to help you take the necessary steps to quash the warrant and deal with the underlying case first. The best lawyers can be found by word-of-mouth, not billboards, city buses, or day time and late night TV commercials.
Possible. The computers are linked between the warrant division and the drivers license agencies, but it really depends on a few factors: the county that issued the warrant, whether it is a misdemeanor or felony warrant, and whether you are applying for a license in a county different from the one that issued the warrant. I wouldn't chance it though without an attorney.