Asking questions in the negative is certainly a Czech thing, but it is not a very common English thing. Generally, we ask questions in the positive. Usually when we ask a question, we don’t know the answer – which is why we’re asking the question in the first place! So if we wanted to invite someone for a beer, we’d say, „Do you want to go for a beer?“
We’d also use a positive, for example, to ask, „Do you have a brother?“ or „Have you got a dog?“, or for the majority of questions we ask. The only time we would use a negative is when we already know the answer and we are surprised by it. So, if you heard that your friend didn’t want to join you and your other friends in the pub that night and you were surprised by this, you’d say, „Don’t you want to go for beer? Why not?“
It is like saying, „Really? Are you sure?“ Confused? Here’s both positive and negative versions used in a dialogue:
A: Do you want to go to the pub tonight?
B: No thanks, I fancy a quiet night. David asked me earlier if I wanted to see the new Star Wars film but I wasn’t interested.
A: Don’t you want to see it? I’ve heard it’s amazing.