You are correct in your analysis. The first は establishes the topic as この映画館で ("at this movie theater"). What came prior in the conversation was not talking about この映画館. Then, 水曜日は implies that the price is what it is on Wednesday, as compared to another day / other days when the price is something else (contrastive marker).
PLACE では means "at PLACE", so its saying
At this movie theater, you can see a movie for 1,000 yen on Wednesdays.
It does imply that it isn't that price on other days, but that comes from the context and not the sentence structure itself. Its not strictly a contrastive, its just the standard subject marker.
I think I might know what it means, but I apologize if my explanation is not that good.
I believe the verb here is 居る (iru), thus, your sentence would translate like "There's no way that there is a cat (or cats) that sit in such (stiff) manner."
いる is not written a lot of times with its kanji so maybe that's why it was not so clear at first. In the sentence,...