It depends. NJ will allow you to have a tax credit to another tax district (even a local district) claimed on your NJ return, but the credit is only up to the point where NJ is taxing the same income. Please see this NJ website for more information: NJ Division of Taxation - Income Tax - Credit for Taxes Paid to Other .... On the site you'll see this excerpt:
New Jersey requires you to pay tax on all of your income, regardless of where it is earned. The credit reduces your New Jersey Income Tax liability so that you don't pay taxes twice on the same income. This is not a refund of the taxes you paid to another state or city. Your credit cannot be more than the amount you would have paid if you earned the income in New Jersey. (Italics added)
As explained on the site, NJ cannot refund you for taxes paid to Philadelphia, but will give you a credit up to where NJ is taxing the same income. From your question it seems like NJ is not taxing the same income very much (or because of other tax deductions and credits you have a lower tax on this income), or at least nowhere close to what Philly is. But that is all of the credit that NJ will be able to give you, as explained above.
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Yes
No
