Now I think of that, are there taxis in Przemyśl?
Yeah they're quite common their is a taxi rank at the train station (Near the a few buero de change's [kantory])
Just asked my girlfriend (Who is from Przemyśl) they're buses to Tarnawce. You might want to look up bus routes to Krasiczyn castle as its on the way.
The town has a very good bus service with three bus company's that I remember (DamiTrans, PKS & MZK) PKS Definitely serves this route.
Buses cost 2.50Z£ on the bus or in shop tickets are 2Z£
As for cemetery, if you are referring to the very large one on the hill it is also served by bus and there is a beautiful bar across from it, there's a outdoor area at the front beside the road (Across from a bus stop) with somewhat of a metal frame covered from view by loads of grape vines growing down, it looks magnificent and when I was their last week the grapes where just starting to get big still green.