grammaticality - Collective nouns and subject-verb agreement: general rule or arbitrary?

A newspaper ran this headline recently:

(1) Police crack down on IAC protesters. [emph added]

Why did it not read:

(2) ? Police cracks down on IAC protesters.

I have found instances of "police cracks" in newspapers: "Police cracks whip" and "Chesterfield police cracks down on drunk drivers". However, Google's Ngram Viewer suggests that "police cracks" is significantly less frequent:

I think that the difference between "Police crack down" and "Police cracks down" is influenced by subject-verb agreement and that the difference in this example reflects the grammatical number of the verb's subject. Here, "cracks" is inflected for singular number, which implies that its subject is singular, and "crack" is inflected for plural number, which implies that its subject is plural. E.g.:

The army cracks down on IAC protesters. [singular]

The armies crack down on IAC protesters. [plural]

The confusing thing about (1) and (2) is that the subject, "police", looks like it is singular; the plural form would be "polices", but I have never heard this form (for the noun).

It sounds like police fits the definition of a collective noun, which Wikipedia says is "the name of a number (or collection) of people or things taken together and spoken of as one whole. For example, in the phrase 'a pride of lions', pride is a collective noun." Police fits this because it refers to (i) some relevant police force or (ii) some relevant group of police officers, which are both collections of people taken as wholes. It does not refer to a single police officer.

So one might conjecture that verbs whose subjects are collective nouns are inflected for plural number. However, it sounds like group also fits the definition of a collective noun because it refers to a collection of individuals taken as a whole. And I think that both of the following sound acceptable.

(3) The group crack down on IAC protesters.

(4) The group cracks down on IAC protesters.

The above conjecture also doesn't explain why it is sometimes okay to use "police cracks".

My preliminary questions: Do (1), (2), (3) and (4) all sound acceptable to everyone else? Are police and group both collective nouns?

My main questions: If (3) and (4) are both acceptable and police and group are both collective nouns, then why does (1) but not (2) sound acceptable, or at least why is "police crack" better than "police cracks"? How do you determine the correct conjugation for a verb whose subject is a collective noun? Is there a general rule, or does it vary from case to case?

My secondary questions: Does the behavior of (1) and (2) have to do with synesis? Is using police to refer to the police force more like a synecdoche or other kind of rhetorical trope? Does it matter if you add "the":

(5) The police crack down on IAC protesters.

(6) ? The police cracks down on IAC protesters.

I ask these secondary questions because I find it interesting that policeis, to me, a near synonym of police force, but police force (Ngram verb comparison) behaves oppositely to police (ngram verb comparison) when it comes to subject-verb agreement:

(7) ? The police force crack down on IAC protesters.

(8) The police force cracks down on IAC protesters.

[Note: the question mark at the beginning of an example indicates questionable grammaticality.]