I was on an F1 visa in 2011 pursuing my post-graduate degree in Pittsburgh. During the summer, I worked in New York for 10 weeks on F1-CPT. I was however residing in New Jersey.

1) Should I file Pennsylvania and Pittsburgh city taxes as I have never earned wages in Pittsburgh?

2) If so, am I a resident / non-resident of Pennsylvania as I am an international student?

3) Pennsylvania has a reciprocal agreement with New Jersey. Would this help me in any way? Am I a resident / non-resident of New Jersey?

4) Should I even file New Jersey Taxes or stick to NY taxes as a non-resident and get exemption for NY city tax?

4) What other state taxes must I file?

Your F-1 status makes you NON-resident in all three states.

Since no money was earned in Pittsburgh, no city or PA state return is required.

You DO need to file NJ and NY returns, but the tax credit you will get for paying NY state tax will completely offset any NJ tax.

If you want my professional help, you can find my email address in my profile.

You worked in NY so you must file NY tax return. You do not pay NY city tax as you did not live in the city. Also international students are nonresidents for the purpose of city tax.
You lived in NJ so you will also file NJ tax return if your income is more than the NJ filing requirement. Also claim credit for taxes paid to NY.