/ A Polish bank that doesn't rip u off.....
PKO BP is definitely Polish since it belongs to the state.
But does it matter, who owns the specific bank? I don't think so. What I would like first at a customer is the quality of service, not the country of the bank.
Also most of these banks used to be Polish, they were created either in the process of division of the NBP (Polish National Bank - currently responsible only for taking care of all the money on the market and supervision over all the banks) in 1989 - for example PKO BP, ING, BPH - most of the biggest banks, or were created from scratch as private businesses - like mBank. Only Pekao SA is a bank which existed before 1989 - and was also originally Polish.
Therefore they employ really a lot people in Poland and also pay taxes here.
Charging for checking the balance in a cash machine is typical especially for the online-oriented banks. From what I know, for example Pekao SA doesn't charge for this.
Debit card without monthly fee - yes, there are such accounts, but then you usually have a given minimum amount of card transactions which you have to make not to pay. If you use a card, then you don't pay for it. If you almost don't use it (using means making transactions in shops, not withdrawals in ATM's), then you have to pay. Or it might be also so that the card is totally free, but you pay something just for having the account. Although it might be also so that if you have a regular income to your account, then you don't pay anything for both the account and the card.
There is only one bank where the account is totally free - Smart Bank - but it's online only and you may have problems if something doesn't work (you have to call their hot line, wait for getting a connection with a consultant, and waste money for that, the consultant will probably unable to do anything other than just accepting a complaint, then you wait until they decide about your complaint etc).
There are banks which have offers for free withdrawals from ATM's of other banks.
WBK seems to have quite a good offer, if you want free withdrawals from all the ATM's.
mBank might be also good in terms of the prices, or T-Mobile (it's actually an offer of Alior, just branded by T-Mobile), but they are online only (mBank have some brick-and-mortar points, but not many, only in bigger cities, and only few of them allow you to do something more than just signing a new account or credit contract; T-Mobile have such services in some of the T-Mobile shops, also only in bigger cities), which means you will probably have to use a Polish-only web interface and sometimes use a Polish-only hotline.
mBank has "eKonto z darmowymi bankomatami", where if you make transactions by card for minimum 200 zł for a month, you don't pay absolutely anything. And you have free withdrawals, as the name says, from all the cash machines in Poland. In T-Mobile it works in actually the same way, but the monthly fee for a card if you don't do these transactions for 200 zł is 6 zł, not 7 zł like in mBank.
In PKO BP you have "Konto za zero", it's free if you make card transactions for at least 300 zł in a month. Withdrawals are free only from PKP BP ATM's, but they have probably most widespread ATM network.
But mBank has "eKonto standard", where it's enough to make 5 card transactions in a month (so just whenever you do shopping, pay by card) to make the account totally free, and they have free withdrawals from the ATM's of: mBank, BZ WBK, Planet Cash and Euronet. Those together are definitely a wider network than ATM's of PKO BP.
PKO BP is, though, definitely a brick-and-mortar style bank, you don't have to do everything on a phone. You just come to the bank in a street and do everything there. But still you need to find such a point of this bank in which the employees speak English.
What is weird in Poland is that most of the banks don't offer any online interface in English.