I put "we welcome you". I got rapped upon the knuckles. I suppose that would be 'witamy was'
It's not that obvious who will pay. If you want to clarify it you add: „Ja stawiam/ja płacę”
'Zapraszam(y)' is the most commonly inappropriately translated phrase from Polish, due to the insistence that personal interaction is not defined by culture. So Poland is full of 'we invite you', until the native EN speaker is ready to retch.
I literally thought about this repeatedly when I was last in PL - I saw a sign for a store that said, to paraphrase: "Mamy pysznych hotdogi, zapraszamy!" "We have delicious hotdogs, we invite you!"-But I thought about how dumb that sounded in english and this is where "translation" and interpretation differ - So, depending on the context used, and in this case, I would interpret it as "We have delicious hotdogs, come on in!"