i have a polish passport and can speak the language...
It won't really matter as far as salary. It will help you get a job and be a more attractive candidate but it's not like they'll give you an extra $1k a month because you're a native speaker that's also fluent in Polish. You could have a PhD and teach at the best uni in Katowice and you'll still receive a salary that's at best average by Polish standards. Teachers simply don't get paid much in Poland. It's not like Germany or even Kazakhstan where native English teachers can make $80k a year with only 10% income tax taken out if they land at one of the elite schools that politicians, business people, etc. send their kids to.
Since you have experience, focus on private British and American schools. These tend to have the best salaries and since you already have experience, are a native speaker, speak Polish, and have certification you'll be able to land a job at one of these schools. The pay is going to be way better than some local public school.
As far as when to come, idk how hiring goes in the middle of a semester. I'd imagine though like most schools they'd fill positions a few months before the start of a semester though.