You would need to file a PA return to report the PA income. Look at the instructions for PA and WV to see which gives the credit to the other. My seat of pants guess is PA gives credit for WV tax paid on same income, but you can look it up. 

Unless PA has a reciprocal agreement with WV (like PA and NJ have), then yes as above.

(Google is your friend.)

What does your paid tax professional say?

In order to get any PA withholdings recovered, you will need to file PA.

Your previous question was posted under ProSeries. This is Lacerte. It helps to stick with the section for the program you are using for your clients' tax prep, so that you get specific help with that software.