You capitalize 'police' after the department name, where the word is part of the department name, as in, 'The Somerville Police Department is looking to recruit more policeofficers.'
No, not unless the word 'police' was part of the official name being used (for instance: United State Park Police - New York City Police Department.)
no
Yes, you do capitalize the word department when it directly follows the name of that department. This is the case when signing letters or referring to specific departments in emails or in writing.
Yes.
NYPD (New York police department
No, "police" isn't a proper noun in this case, if I read your question correctly. It would be proper if you wrote New York Police Department or something like that.
You should only capitalize it if at the start of a sentence or part of a title/name (Eg. United States Department of the Treasury).
No it should only be capitalized if it precedes a name.
Police is a common noun. Proper nouns name a specific police officer or a specific police department. Examples: Officer Glen Martin The Glendale Police Department
It is capitalized at the beginning of the sentence or when it forms part of the proper noun. Example: The US Federal Police
Yes.
Internal Security Department
They are officially known as "The Hong Kong Police Force."
Yes, but they do not share the information.