I am a green card holder since 2002 but I am traveling outside US most of the time.
What is the period to accumulate inside the US in order to apply for US passport and how long is the waiting period /other conditions noting that I live in NY

You can't 'accumulate' anything, once you become naturalized and have received your Certificate of Naturalization, or become an American Citizen, then you can apply for a US passport.

www.immigrationdirect.com

You should have no problem travelling outside US if you have your homeland passport with your visa inside it to re-enter.

You must be in US 50% of the time since you become permanent resident.