"There are no police boxes anywhere."
It is okay but I would use 交番はどこにもありません if you put 交番 in front. Sounds more natural.
It depends on context. There is a case for either, depending on what you are emphasizing.
It shouldn't be はありません、instead of がありません？because when the verb is negative, the particule が changes to は?
I'm not a native speaker, but I'm specializing in Japanese in college. As far as I know, that's not the general use for the particles (as in negative/affirmative function). They kinda act as "determiners", when you select something with は, the focus of the sentence will be on its predicate (and not the selected subject), and the opposite for が, when used the subject will be the focus, often used when you're introducing something/someone.