It all depends weather what you plead guilty to is crime or not. It seems like a it's a small regulatory offense, and probably a violation. I 'd say you should be ok.
Att. number 917-885-2261 This advice does not create an attorney client relationship. No specific legal advice may be offered by the lawyer until a conflicts check is undertaken. Information sent through a web form or via email may not be treated as confidential. Please accept my apologies for spelling mistakes. Law Office of Alena Shautsova www.shautsova.com www.shautsova.com www.russianspeakinglawyerny.com
It depends: assuming you are not on probation, and assuming it is not a crime of moral turpitude, you should be fine. Get a consult from a local immigration attorney.
To qualify for naturalization you need to show good moral character for the last 5 years. Even if you were not convicted for shoplifting, if anywhere in the record you admitted to the elements of the crime immigration could use that to make a determination on your moral character. Probably that's the reason they are still looking at it, to see if anywhere on the record appears an admission.