Based on information provided, you are an LPR [green card without conditions] and you got the green card based on marriage to a US citizen whom you are now divorced. If correct, you do not have to notify CIS of your divorce and you can legally remain in the US for the rest of your life, subject only to obeying all US laws. You do not have to become a US citizen. In fact, many LPRs spend their entire lives in the US in this way. But some LPRs decide to become US citizen and you may choose to do so as well by filing a Form N-400 citizenship application. You can do this 5 years after you got your green card. Your divorce is not a bar to your naturalization. Finally, one of the benefits of green card status is you may travel outside the US and return at any time. and any overseas trip lasting less than 180 days is fine. Good Luck.
Answered on Oct 10th, 2013 at 2:55 PM