to be able to maintain a green card status, you have to enter the US at least once every year, but to be able to apply for citizen ship you have to have a continuous residency , which is 2 and I /2 year out of the last five years with no gap outside the US of 6 months or more. I suggest to go to uscis.gov and download the N-400 form to have a good idea to what to expect when you are filing for your citizen ship.
about paying tax, you will not pay tax up to (91500) if you reside outside the US and you can not be in the US for more than 35 days.
hope this will help.
F.D