DUI conviction and application for citizenship is DUI a deportable offense

You would have saved yourself a lot of worry and trouble if you had sought out the advice of an immigration lawyer.
A DWI in and of itself will not cause you to loose your shot at Citizenship, assuming you have a green card.
It is not a deportable offense, however you need to address the issues with an immigration lawyers (you can find a bunch of good ones in your state right here on AVVO.Com) If you are without papers or overstayed your visa, deportation is possible anyway, hence get to a immigration lawyer right away and then you will not have to worry anymore.

Please take a look at the link to the Naturalization Guide on this website.

You should speak to an immigration attorney before you apply again for citizenship. It would be a good idea to first get a copy of your criminal record from all the courts you were convicted so that the attorney knows exactly which convictions you have. This will help to see if you are in danger of deportation for your crime.

Abandoning your application should not be a problem. But talk with an attorney and show her/him the letters you received.

First call an immingration attorney. But generally if you are convicted of one misdemeanor that is not a crime of moral turpitude and do not spend over 6 months in jail it should not affect you citizenship application. If it is a felony, or a crime of moral turpitude, or you spend six months in jail it will affect your citizenship. But if you have more past convictions it may also affect your citizenship. Call an immigration attorney immediately, they will know exactly what charges are of moral turpitude and will assist you with the entire process.