Well do you knoe then by any chance if getting married gives you any privilages at all when it comes to working in the EU or not? (of course considering marring an EU citizen like myself)
Yes.
When entering the EU member state for the first time with your spouse, simply show your EU passport and marriage certificate at the airport or ferry port , upon entry. Within 3 months, register at your local Police station/Immigration centre. That's it, you're done.
Could I also get a green card once married but living in Europe?
No, spousal visa. Which cost a lot.
Could our children, considering they would be born in the US get a Polish citizenship as well?
Yes.
Whats with the username, btw? Detriot is a dump.