... according to The Associated Press Stylebook, or The Associated Press Stylebook says: XXX.

(I hope you're using the 2019 edition or the online version, to be sure you are quoting up-to-date material.)

AP doesn't have a specific style. I see that Webster's New World College Dictionary (which you may get as part of your Stylebook subscription) uses Rhode Island Red, as does Merriam-Webster. I can't speak to their reasoning for sure, but I imagine it's for clarity to distinguish from a general reference to the color.

I'd use the guidance in the composition titles entry. 

If it's a title or a headline, AP style uses single quote marks.

With the hyphens.

The way you have it is fine.

Use the double quote marks.

Crosshairs, per Webster's New World College Dictionary (and Merriam-Webster has similar)

(krôs´)

n. a line or, typically, one of a pair of crossed lines, as of fine wire or hair, mounted in the eyepiece of a telescopic gun sight, surveyor's level, etc. to assist in precise aiming or centering of the instrument: also sp. cross hair –in the (or someone’s) crosshairs targeted (by someone) for hostile or critical action or scrutiny

This isn't entirely style, which is in flux anyway. But for consistency, I'd do: 2 minutes, 1 minute and 45 seconds, 2 1/2 minutes (no hyphen in the last one).

We don't use double quote marks in the answers of a Q&A. Thus, you can use double quote marks around dream team. You also could use no quote marks; I think the term dream team stands on its own. NOTE: Quote marks aren't intended to be used as emphasis. 

The comma always goes inside the quote marks, whether single or double.

As we say in the hyphen entry: Use of the hyphen is far from standardized. It is optional in most cases, a matter of taste, judgment and style sense.

One of the pieces of guidance is to refer to Webster's New World College Dictionary. Many word combinations aren't listed. But Webster's does show single-payer with the hyphen.

Yes, the hyphen is good.

It may vary from case to case. I'd use them here.

Two words.

Not sure what the use would be as a noun. Can you give an example? Perhaps there's an OK time to use it as a noun, but we're not thinking of one at the moment. A person is not an LGBTQ, for example.

Yes, hyphenate for clarity. (It's a judgment call and could go either way., though.)

Informally, lowercase. On second reference, wording such as the military force authorization would work. We wouldn't use the acronym at all. And the same approach for other authorizations: Uppercase if it's the formal name; lowercase and a shortened version (but not the acronym) on later references.

For the formal act: the 2001 Authorization for Use of Military Force, which Congress passed after 9/11.

We tried in the past year to devise some consistent approaches to questions like that. We ran into entanglements along the lines of what you refer to. Failing to come up with reasonable, consistent solutions, we put it on the list of what we'll try again to tackle in the coming year. This also plays into other areas, such as academic departments, law enforcement units, governmental committees ... the list goes on. It's one of the (many) questions that aren't nearly as simple as they might seem at first.

I realize that's not much help right now!

With the decimal  is correct. But it's a bit of a cliche and we don't use it very often.

This is similar to your previous question, right? Here's the entry on academic degrees.

Yes, there definitely is confusion in that entry as well as in the pre- entry. It's been that way for years, and no one noticed until recently. We need to address it, but haven't had a chance yet to do so. So I don't have an answer yet.

We typically use the shorter version: Marine Capt. John Smith.

Yes. that's absolutely right. You have to be careful, though: Sometimes a reader may not understand that you intend those two things as one thing and thus may not get the grammar. It's case by case. I'd use the plural in this case, but that's more my instinct than anything else.

First, here's the entry with style on the degrees.

Example University offers 30 master's degrees, 26 bachelor's degrees and 34 associate degrees. But I think it's better to specify that you're talking about programs, not degrees: Example University offers 30 master's degree programs, 26 bachelor's degree programs and 34 associate degree programs.