Yes, in Poland police can and do patrol in plain clothes, there will always be 2 of them, it can also be police and military, or police and local deputy (town guard).
Polish police can stop and frisk anyone, under any suspicion, tho they have to say what was it, and if you are not aggressive or if it would endanger them they can not show the badge (until proper car unit arrives). If you act normal they will show you the cross (badge) and police ID. (see below) They will be armed.
Routine check consist of noting your Name, Occupation,Birth date and Birthplace checking of your ID, and if needed may contain asking what are you doing and why.
If you feel unsure if they are indeed officers of police you can say that you want to confirm if they are ones and call the police to prove it. (they will either check if their id's match or send normal patrol to you)
The police will never keep your ID, they will never ask you for money, they will never take your passport. You can deny having them but it will result in longer questions - Names of parents and/or your ID number if you have one.
Refusal of cooperation is a minor offence so if you act like dick you may get a ticket.
All tickets in Poland are paid thru banks. Nothing goes straight to policeman.
List of things police will stop you for:
Jaywalking - anywhere there is not a zebra. but on minor streets you can cross at the end of it (if there is not a zebra within 100m).
Turning right on red (if there is no green arrow) - that's for americans
Crossing on Red - Even if there are no cars.
Being drunk - that can also get you arrested.
Driving drunk - that will get you arrested.
Drinking in public outside the bars.
Being alone underage.
Smoking near random people.
Riding public transport without ticket.
If you get checked without problems don't fear to ask them for directions or nice restaurant or anything.