Note that the w in the polish sentence should be pronounced differently. The way it's pronounced now ("wu") is the way it's pronounced when you spell the alphabet.
"There are no movie theatres in my district" , what's wrong with that? I think it is more natural to use plural when describing absence, in this case anyway.
Why can't it be I don't have. I am not English so it's more of a english question I think
That could be a proper sentence ("I don't have a cinema in my district"), I believe, but that's too far from the original Polish sentence.
In American English, "district" is rarely used except to refer to "school districts"--the maps that determine which schools children attend. In the context of this sentence, we'd be more likely to say "in my area" or "in my neighborhood". Would either of those be acceptable here?
I think that both "neighborhood" and "area" are too vague. "dzielnica" is something which has clear borders set on the administrative level. For "area" and "neighborhood" I would go with "okolica".
I have to agree with fenamanaal, I wrote I do not have a cinema in my district, think that should be accepted, as nie ma translates literally to I do not have. And I think correct English..
"Nie ma" doesn't translate to "I do not have". That's "Nie mam". It could potentially translate to "He/She/It doesn't have", but in such a construction it just means "There is no".