Should I check single or separated on my n400 form if my husband and I are estranged and he does not live in the US?

Generally, a person who became married, never divorced and never was the subject of a court-ordered legal separation lawfully is neither "single" nor "separated," and instead remains married (although may be living apart from a spouse). That is only one example of how immigration forms and their instructions, and even a review of the statute and regulations, can be inadequate to properly proceed with a naturalization petition. Errors in preparing the forms and in supplying supporting a full set of supporting documents can cause significant delays or even more harsh consequences. It would be wise for you to consult with an immigration attorney who, after learning all of the relevant information, could advise about eligibilities, options, and strategies to attain your goals, and who then could offer legal representation in the often complex application process.