My fiancee lives in the US and is a US green card holder and about two
years away from being applicable for citizenship. We plan to get
married in my country (Kuwait) after 6 months and plan on living here.
But I'd like her to have US citizenship eventually as it eases local
immigration laws. I have a few questions:
1. Would her eligibility for citizenship be affected if she lives in
Kuwait for a long time? Would it help if she made occasional trips to
the US? How frequent should they be?
2. Since we're getting married in Kuwait, does she have to inform the
US immigration authorities as well that she got married? Will it
influence her citizenship application in any way?
3. I'd like to get a green card myself, since I'll probably make
frequent visits to the US and we may decide to live there later on.
Should I apply for the card after she gets citizenship or before?

The U.S. grants citizenship to those who truly love and respect our
country.  Citizenship is not for those who want to use it for their
own convenience.  You should ask thise question of INS (or whatever
they call themselves these days).

There is a five-year continuous residency requirement for those
seeking US citizenship (
http://www.uscis.gov/graphics/services/natz/general.htm ), so your
first plan would probably not work.