Any American grocery store has these products
sledz, I think valmoe1 is an American living at the present moment in Poland, so your advice isn't helpful :)
You can find in any store with food:
baking soda = soda oczyszczonabaking powder = proszek do pieczenia(they aren't exactly the same as American, baking powder in Poland may have slightly different ingredients and baking soda probably no additives, but I think they serve the same purpose)
aromat waniliowy - vanilla fragrant oil (liquid)
cukier waniliowy - a mix of sugar and vanilla fragrant (could be vanilla pods or extract, but usually available the cheaper versions use synthetic vanillin)
wanilia - look among spices (powdered vanilla - in small paper bags, a popular producer of spices in Poland is Kamis, but you can buy other, just avoid those really cheap, below 1 złoty), you can also buy whole dried pods (quite expensive, about 10 zł for a pod)
cream of tartar - I can't help you, I have no idea what it is.