My Spouse and I live in different cities, will this affect the approval of our petition?

It may or may not.  The usual position is that married people live together, so the USCIS expects you to show a joint residence.  If you do not, it raises a red flag.  Yet there are several good reasons why a couple may be living apart.:  perhaps one of them is in school; perhaps a job has taken a job in another city.  

In a case like this, it is important to document other things that show your joint life.  You should also plan to show (document) how you and your spouse communicate – daily phone calls, text messages, emails, visits.  You should also be ready to give a clear and concise explanation.

I am a US citizen and I live outside the US.  I want to petition for my wife.

You may indeed petition for your wife.  You should watch out for showing your domicile.  This matter comes up when it is time to apply for a green card and you are needed to show that you will be able to support your spouse – on the affidavit of support form, precisely.   The issue is whether you have domicile in the United States.   Domicile means a place you have your permanent home (your heart) and where you always mean to return – you can show that you have your domicile in the US by having a US address, paying your US taxes, visitation from time to time.  If you are not able to show domicile in the US at the time of filing of the application, your wife's adjustment (or immigrant visa) application will be denied.  

My Green Card came and it says it is valid for two years, what does this mean?

Your green card is valid for two years because on the day it was given, your marriage to your US citizen spouse was less than two years old.  It was therefore given with a condition attached to it.  You and your spouse must petition to remove the condition on the second anniversary of the grant of the green card.  You may file the petition any time from 90 days before the date of that second anniversary.  The application to remove condition should be accompanied by the same type of documents which you used for your initial green card application, but covering the period between the grant of the card and the time of the petition to remove condition.