In short No.
There are laws that if you sell to anyone within a particular state in the U.S. you must obey each state's tax laws. However for the majority of the tax laws the exception (loop hole) is in the digital services realm - where you can claim income as 'advisory / non-physical services' and not pay in any of the states except for your own. If you are incorporated in a particular state you do have to pay taxes there - regardless of where you 'conduct business from' you are operating out of PA.
I don't think you have to pay federal (unless your income surpasses their bracket which I think is $100k+ for those residing outside U.S. i.e. military contractors) But you do have to pay PA state income taxes that's why is wise to incorporate any form of business in states with the lowest tax brackets such as Delaware, Wyoming, Nevada...

Yes, you need to report the income from your single member LLC. If you live abroad and qualified for the earned income exclusion, then you may be able to exclude a portion of your earnings. A U.S. citizen is required to report all of their gross income, derived from whatever source, even if they live outside of the United States. If you live outside of the U.S. and meet either the bona fide resident test, or the physical presence test, then you may be able to exclude a portion of your earned income from U.S. federal income taxes. However, you will not be able to avoid self employment taxes on the net earnings passing through from your single member LLC. The U.S. federal tax rules for U.S. expats can be incredibly complex. I would highly recommend you seek the advice of a competent U.S. tax adviser that specializes in U.S. expat taxation.