Now Poland's in the EU I have no real idea about full residency requirements (I'm a UK citizen).
Off the top of my head ... it's going to take you years! I never got it.
Hah, I remember applying for temporary residence a few years ago - 37 attachments, hours lost, long delays and loads of money down the drain.
Now, it's 30-odd zlots, lasts 5 years and is prepared with extreme efficiency. What a transformation!
As for fitting in, well - you're not white, so that works against you with a minority of lunatics. I'm only an obvious foreigner when I open my mouth, thank goodness. Just be prepared to be polite an dmost people will be nice back.