Do I qualify to apply for a green card if I have a warrant for a DUI?

To have an outstanding warrant means when you apply for green card, your biometrics (fingerprinting) will show CIS that you (a) you have an arrest record and (b) you have open and unresolved criminal charge(s) against you. CIS will not approve your green card or even work permit unless you bring a certificate(s) of disposition of the DUI cases. Therefore, you must first hire a good criminal defense lawyer to resolve your DUI cases and warrants. DHS takes dim view of DUI offenders who, it believes pose significant danger to lives and property of US citizens. Depending on how your DUI case is resolved, you may or may not be able to get a green card In fact, you may be deported if you are convicted of the DUI. So, it is important to also hire an immigration attorney right away to work with andf advise the criminal lawyer in helping him map out an outcome of the DUI case in such a way that will not result in your deportation from United States.

You need to bring the full record in to an immigration attorney prior to filing, and you will need to deal with the warrant.

Adjustment of status is discretionary. Yes, I would say you could be denied and I'd give the warrant top priority. Fix that problem first. You should consult an immigration lawyer with your court and police records before you file for your green card.