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New York State Criminal Procedure Law §160.55 provides for the return of fingerprints, photographs and sealing of a defendant's conviction of a violation of the penal code or a traffic infraction.
However, driving while "impaired" by alcohol in violation of Vehicle and Traffic Law § 1192(1) is considered a violation, but for special reasons, such violation convictions cannot be sealed.
So no this can't be expunged under NY law.
Yes, it will stay on your record indefinitely.
And yes, it is a traffic infraction, not a criminal violation so you can honestly answer that you have not been convicted of any misdemeanor or felony if that is the only thing on your record.