I'd lowercase both the singular and plural, modeling after this entry:

Capitalize as part of a proper name: Lake Erie, Canandaigua Lake, the Finger Lakes.

Lowercase in plural uses: lakes Erie and Ontario; Canandaigua and Seneca lakes.

Our style is M.D. Here's the entry:

M.D.  A word such as physician or surgeon is preferred. The periods in the abbreviation are an exception to Webster's New World College Dictionary. See doctor and academic titles.

The bottom entry, which uses the comma, is the Webster's New World College Dictionary version. You have signed up to receive the dictionary entries as part of your Stylebook subscription. A search for Martin Luther King shows the below, with the Stylebook header at the top and the dictionary header at the bottom. We often concur with the dictionary style. But at times, such as this one, we differ.

We don't italicize anything in material for publication. I'm not aware of any major style that italicizes institutions or nonprofits.

Yes, use question marks within the quotation marks for both of those. And remove the period at the end: 

With dedicated staff, tools and methodology, we help clients maintain a line of sight into the questions  “am I compliant locally in every jurisdiction where I have operations?” and “who has the most recent filing?” 

We use lowercase. You can differ, of course.

We don't use the term browns. A great deal of detail is in our race-related coverage entry. I suggest reading the whole entry.

I'd write it out in that use. I'd also hope that there soon becomes a generally accepted shorthand for the facility!

Yes, that's fine by AP style, for Ivy League schools or any others.

I'm not seeing a trend away from hyphenation. We generally hyphenate modifiers of three or more words, as noted in the hyphen entry:

Generally, also use a hyphen in modifiers of three or more words: a know-it-all attitude, black-and-white photography, a sink-or-swim moment, a win-at-all-costs approach. 

This is the spelling that we got directly from his family. We try to be precise and follow the family’s spelling. 

Use Rock Hall if needed in a shortened reference such as a headline.

We use the marks just for people's names. Not for company names. Certainly you're welcome to do otherwise, if you prefer.

No, we don't recognize organizations as people. Use that, not who or whom.

We refer to them as third-year law students.

We dislike it intensely, and it's not recognized as a noun by either Webster's New World College Dictionary or Merriam-Webster. Sounds like jargon, which we avoid.

No hyphens in that use.

We generally spell it out on first reference: former President Barack Obama's administration.

None of those are actually words, so it's a little hard to decide a style for them. I'd follow our general advice that no hyphen is needed. But I'd also avoid most of those constructions.

The rules in prefixes apply, but in general, no hyphen. Some examples:subbasement | submachine gun
subcommittee | suborbital
subculture | subtotal
subdivision | subzero

Generally we use the style preferred by the company, although there are exceptions. I've deleted the previous answer about CliffsNotes.
Here's the entry:

For a company's formal name, consult the New York Stock Exchange, Nasdaq or filings with the Securities and Exchange Commission.

Do not use a comma before Inc. or Ltd., even if it is included in the formal name.

You must include the full company name somewhere in the story. This ensures the story will be among the search results on major websites.

The formal name need not be used on first reference – for example, Costco is acceptable for Costco Wholesale Corp. – but it should be contained in the body of any story in which the subject matter could affect a company's business. For example, include the corporate name in a story on an earnings report, or in a story on a plane crash that could affect the airline's stock price. However, the corporate name might be irrelevant in a story about a political candidate's appearance at a local retail store.

If "The" is part of the formal company name it should be included. For example: The Walt Disney Co.

Generally, follow the spelling preferred by the company, but capitalize the first letter of company names in all uses: e.g., Adidas, Lululemon. Exceptions include company names such as eBay, which have a capital letter elsewhere in the name. However, company names should always be capitalized at the beginning of a sentence. For corporate news, AP may use the legal name from the Securities and Exchange Commission filing rather than a company's preference.

Do not use all-capital-letter names unless the letters are individually pronounced: BMW. Others should be uppercase and lowercase. Ikea, not IKEA; USA Today, not USA TODAY.

Do not use symbols such as exclamation points, plus signs or asterisks that form contrived spellings that might distract or confuse a reader. Use Yahoo, not Yahoo!; Toys R Us, not Toys "R" Us; E-Trade, not E*Trade.

Use an ampersand only if it is part of the company's formal name, but not otherwise in place of and.

Use the lowercase unless it is part of the company's formal name.

We're using Baby Yoda.

We use this dateline: TAIPEI, Taiwan  – Story starts here. 

Here's the entry:

When used alone, it refers to the nation that includes the mainland, Hong Kong and Macao. Use China in mainland datelines; Hong Kong and Macao stand alone in datelines.

Use People's Republic of China, Communist China and mainland China only in direct quotations or when needed to distinguish the mainland and its government from Taiwan. Use Red China only in direct quotes.

For datelines on stories from the island of Taiwan, use the name of a community and Taiwan. In the body of a story, use Taiwan for references to the government based on the island. Use the formal name of the government, the Republic of China, when required for legal precision. See “One China” policy.

Yes.

That's correct.

Yes.