Nowadays you can buy a ticket in virtually every bus or tram (just be sure to enter the first coach). Be aware that some of them only accept credit cards, some only coins and finally there are some that accept any payment.
You can also buy tickets through several applications, I'm normally using SkyCash - you have to provide your credit card number in ...
From a tourist info website:
One-way ticket for a municipal bus or a streetcar (tram) is 4.6 zloty (an equivalent of roughly one euro). You can buy it at many newsstands and from ticket machines at downtown stops and in some buses and tram cars. Drivers sell 90-minute tickets worth six zlotys. Immediately after boarding you should put the ticket yourself ...
I have travelled to Poland through Germany and noone batted an eyelash even or asked anything. I was born there and my CAN passport clearly states my place of birth. :) I don't go directly however because I know that I will have issues as I do not own a PL passport.
From the question I assume you are talking about an
extension of a residence permit issued to a spouse of an EU-Citizen
You have applied for the extension, which has not yet been issued, and the previous permit has in the mean time expired.
The present permit is a
residence card for family members of citizens of the EU or of the EFTA ...