I don't know all the laws regarding PA hunting and out of country residents, but if you move back here I would assume after a certain period of time(I think 6 months) you would become a resident since you were born here. If such is the case you would only have to complete a Hunter Safety Course and get your general hunting license which is basically a license to hunt small game, turkey and deer(buck only). Then you can get other tags like bear tag, waterfowl stamp and migratory game bird licensse(allows for hunting ducks, geese, doves, etc.).
Here's a link to the
Pennsylvania Game Commision
Go to the website and research it for most of your answers....if you cna't find the info there shoot them and email or call.
As far as firarms and such, I have no idea since your out of country. Good luck and welcome to the boards. This is the best place on the net that I've found to share info and BS about our favorite sport.