1. Your military home of record is PA so PA is entitled to tax the income. Under the Servicemember Civil Relief Act (SCRA) VA will only tax VA income. This is ordinary income with normal PA tax for whatever portion you decide to take now.
2. The PA inheritance tax is charged on the estate return. You didn't mention an estate. The executor is handling the estate return and will file it where the decedent lived and owned properties and give you a k-1 for any taxable distributions from the estate when it is settled.
I am very sorry for your loss.
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