It's born of necessity.

Here's the entry. Some Ask the Editor responses may have varied and I will delete those.

Describes foods without wheat, barley or rye grain, the three groups of whole grains that naturally contain the protein gluten. Usage: He ordered gluten-free pizza; the pizza is gluten free.

That should be ensure. Here's the entry:

Use ensure to mean guarantee: Steps were taken to ensure accuracy.

Use insure for references to insurance: The policy insures his life.

Use assure to mean to make sure or give confidence: She assured us the statement was accurate.

Not in the first two uses of the definition of night from Webster's New World College Dictionary. Here are the dictionary entries:

nighttime n. the time between dusk and dawn; also, the time between sunset and sunrise

(nīt)

n. [[ME niht < OE, akin to Ger nacht < IE base *nekwt-, *nokwt- > Gr nyx (gen. nyktos), L nox (gen. noctis), night]] 1 a) the period from sunset to sunrise b) the period of actual darkness after sunset and before sunrise; also, a part of this period before bedtime [a night at the opera] or the part between bedtime and morning [a sleepless night] 2 the evening following a specified day [Christmas night] 3 the darkness of night 4 any period or condition of darkness or gloom; specif., a) a period of intellectual or moral degeneration b) a time of grief c) death –adj. 1 of, for, or at night 2 active, working, or in use at night –make a night of it to celebrate all or much of the night –night after night every night or for many successive nights –night and day continuously or continually

It's non-life-threatening emergency.

We strongly hope such a use disappears.

I'd go with your second option. Arguments could be made for any of them.

It depends on the use. These are correct:

I and my staff hope you have a good day. My staff and I hope you have a good day. It was a good day for my staff and me. It was a good day for me and my staff. 

We use lowercase: French government. We may on occasion use government of France, though that's wordier and more stilted.

Yes, that still is a complete sentence and needs a capitalized The after the colon.

One might argue that people don't actually have paid family leave unless and until they are actually using that leave, whereas they could have access to it without using it. But I think that distinction is lost in general usage, unless you need to get very specific about the sitution involved. I'd judge each use in the larger context, and decide case by case whether the extra words are necessary for clarity.

If you mean "this is a way to go to San Francisco," then only way is OK. Not ways.

If you mean "I have a long way to go" or "I have a long ways to go," either is acceptable. Some consider ways to be more informal.

We don't have a style on that. In general, AP favors less capitalization. Whichever way you choose, keep it consistent.

It's urges, in the U.S.

Yes, that's good.

Pre-training, following this guidance.

ID'd is fine, assuming the meaning is clear from the context.

We use messenger RNA on first reference, with explanation. Here's an example:

These shots are made with a brand-new technology that injects a piece of genetic code for the spike protein that coats the coronavirus. That messenger RNA, or mRNA, induces the body to produce some harmless spike protein, enough to prime the immune system to react if it later encounters the real virus.  

I'd use fewer in both of those cases, considering the students and machines as individuals and not as one collective mass.

We always use numerals in headlines, including under 10. You could choose a different style, and that's perfectly acceptable. Speaking of headline style, our style for headlines is to capitalize only the first word and proper nouns/proper names. So you're already differing from AP in your approach. That, too, is just fine if that's your choice.

Yes.

No comma there.

If you wanted to start the sentence with the abbreviation (it's not an acronym), you would need to capitalize the n, which would make the already unfamiliar abbreviation that much more awkward. I'd suggest recasting the sentence.

I'd use the hyphen for sure in the second example (people-pleasing habit). The other two are more a matter of preference, I'd say. I'd lean toward no hyphen in quite the people pleaser but yes hyphen in their people-pleasing. Is that totally logical? Probably not. But much about hyphens defies logic. You could use a hyphen in all three and that would be just fine. It would please lots of people.