That would mean "Czy wanna jest w tej łazience?"
It implies (you used 'the', after all) that there was a bathtub mentioned in the conversation and now you're wondering where it is located. "Czy wanna jest w tej łazience? A może w tamtej? Albo w kuchni?" - "Is the bathtub in this bathroom? Or maybe that one? Or in the kitchen?"
The Polish question simply asks whether there is a bathtub in this bathroom (or maybe just a shower). Which sounds like a more probable question to ask ;)
Well, I think I'd just say that the emphasis goes rather at the end, plus of course in speech you have the matter of intonation. Other than that, we would need to discuss specific examples. Like here, we had a normal question about the 'presence' of a bathtub in this bathroom, and karl42 changed it into a question about the whereabouts of the bathtub.
It is the same discussion that we have had before. Yes, it is conceivable that you would use "this" in such a phrase, albeit a lot less so in English than in Polish.
On a side note, I must say that I'm impressed with the standard of accomodation a university student in Poland has...
No, I don't believe that "Is a bathtub in this bathroom there?" is correct. I see two options:
"Is there a bathtub in this bathroom?" (you have no idea whether there is a bathtub there or not)
"Is the bathtub in this bathroom?" (you know that there is a bathtub somewhere in the house, but you don't know where, in which bathroom.
Yeah, it's one of those weird ones - even in the 50s, less than half of houses in England had a bath at all let alone a bathroom! https://www.theguardian.com/society/2018/mar/21/british-homes-without-bathroom-archive-1950. So the whole concept of a bathroom per se in the UK is surprisingly young. The correct answer to your question is "shower room", but due to the influence of americanism, a lot of people would call it (technically incorrectly) bathroom. You'd be disowned by your nation though if you referred to a room with only a toilet as a bathroom in the UK ;)