I pretty much doubt that a parking fine is consider a criminal offence in Poland therefore issuing an EAW is very unlikely. Also, I do not plan to park in prohibited space or way.
First rule of Poland : assume nothing about what is and what isn't seen as criminal. The justice system in Poland is widely accepted as being broken - hence the abuse of EAW's and general incompetence of the courts/prosecutors. It's unlikely that they'll chase you to Austria at the moment (there's no data sharing between Poland and Austria) - but do you really want to have unpaid parking fines hanging over you if Austria/Poland agree exchange of driver information?
As for parking fines being considered criminal - as I understand it, parking isn't decriminalised - if you get a ticket and don't pay it, they're quite within their rights to tow you away.
That sounds great! I might consider this option. Do you know if it's possible to get free parking in Poznań for locals? If so, do I need to have zameldowanie for Poznań? Coz I'm registered in the other part of Polska.
Nope, no free parking unless you're registered locally. I believe the car documents must also be registered to the local address. The best bet is really just to pay up for the guarded parking in the centre - if you tell me where you'd like to park roughly, I'll tell you where you can park.
I forgot to add to the initial post that I'm not a bloody foreigner who would like to take advantage of his alien status :) I don't mind paying for any service what I use, but in my opinion paying for public parking is a legalised pillage by the state / local authorities since I do not get anything in return for my money.
At least in Poznan, the paid for parking exists so that there are parking spaces to park in. It would be complete chaos were parking to be free - Sundays are a great example of this, as are warm weeknights.