Suppose you enter an office that you don't know of their working hours.
Then, you turn and ask,
Excuse me, how late are you going to be open?
To ask the working hour. I haven't said this myself yet, but I was wondering if that's OK to use the pronoun "you" there? I mean, I am asking about the office hours not them. Is that a proper sentence?
Yes.
"you" does not necessarily mean the one person that you are talking about. In fact, the original usage of "you" was always plural, which is why we say stuff like "you are" when using singular you, even though "are" is plural.
In this case, you're using "you" to mean not the specific person, but the office. This is normal, casual English. As long as you're not emphasizing the "you", like "How late are YOU open for?", it is understood from context that you don't just mean that person. (Emphasizing the "you", though, would make it a personal you and not a general one, by shifting the focus to be on the person you're talking to.)
So, yes - your phrase is perfectly fine in casual English. However, I will note that the phrasing "being open" to me, at least, would indicate more something like a restaurant or store, rather than an office. Offices aren't generally just open for people to walk in, so if anything was odd about your sentence, it would be that. Personally, I'd use something more like "Excuse me, what are your working hours here?" or "What's the latest I can get an appointment?". But you'll be understood if you ask how late they're open.
Yes; "you" in this instance means "you guys" more than anything, referring to the office, store, or other place as a group of people.
As a side note, you'd generally say "working hours" instead of just "hour". This is also a common phrase you could use instead, if you thought that your original sentence sounded accusatory: What are your hours?
