Legal Question in Immigration Law in New York

Re: Applying for US citizenship with Criminal Record

You don't need a US Citizenship to travel to Canada, your Green Card is sufficient.

Re: Applying for US citizenship with Criminal Record

If the 2 misdemeanor convictions that you describe did not arise out of a single scheme of criminal misconduct and are deemed crimes of moral turpitude which they would appear to be, you are both removable from the US and inadmissable. Unless you do something that makes the Department of Homeland Security (which used to be known as INS which no longer exists and is now collectively Citizenship and Immigration Services, Immigration and Customs Enforcement or Customs and Border Protection) aware of these convictions such as filing for citizenship or travelling outside of the US, they will likely never know about these convictions. Only you can decide if you want to take the risk of being placed in removal proceedings necessitating you applying for a waiver and having it granted by an immigration judge in order remain this country. Without looking at the totality of your situation, the benefit/risk can't be properly evaluated. More and more, I see people placed in removal proceeedings with very old convictions. NY & the FBI does archive these files.