What mobile phone operator would suit me best?
I think that NjuMobile prepaid card should suit you best
What about the 3G/4G network? I want an operator that can guarantee me near 100% 3G in Krakow, Edge/2G is plain annoying. Where I come from, you would need to pay extra for 4G coverage, is that the same here?
Type the place under "wpisz lokalizacje" field - the map will show you coverage for njumobile network. Currently most popular is 3G network, but 4G in Nju should start this summer 2014. Probably you'll pay something extra for additional benefits of LTE.
I was also wondering what bank would be best for a foreigner who doesn't speak Polish and requires access to internet banking in the English language.
Choose mBank account - you can apply online, all what you need is your passport number, cellphone number, your mother maiden name, etc. - you'll type the address which you currently have.
form.mbank.com.pl/wnioski/ek/index.html - take courier option (translate whole page - it'll be easier)
I am a EU-citizen. Is there besides opening a bank-account anything else that I need to do in Poland upon arrival? I don't think I need to get registered somewhere, or get some approval or visa or something, right?
It depends how long will you stay, and what's your plan in Poland.
Any tips as to how to approach life in Krakow in general, are also always welcome.
Krakow is foreigner friendly. Enjoy your stay!