Form N-400 is the Application for Naturalization used by permanent residents (Green Card holders) over 18 who meet the eligibility requirements to apply for U.S. citizenship.
Form N-600, Application for Certificate of Citizenship, is used by individuals who automatically acquired citizenship through birth to or adoption by U.S. citizen parents, but who haven't received a document to prove it.
Having a criminal background doesn't necessarily disqualify you from Naturalization. However, it can complicate the process. It's important to consult with an experienced immigration attorney if you have a criminal background and are seeking to naturalize.
The process varies depending on various factors such as the individual's case, USCIS caseload, and the applicant's location. On average, it takes between 8 to 12 months from application to oath ceremony