First, in our style we don't put acronyms in parentheses after the full name. We believe that either the acronym should be clear enough to be understood without the parenthetical reference, or it shouldn't be used at all. You can choose to do differently, of course. Here's the abbreviations and acronyms entry.

As for the question of the, that's largely idiomatic. There's no firm rule. When people talk about FERC, or the FERC, which do they say? Go with that usage. 

It probably was just about to be updated online when you submitted the question. It's there now, under the gender, sex and sexual orientation umbrella:

LGBTQ+ (adj.) Acceptable in all references for lesbian, gay, bisexual, transgender and queer and/or questioning. In quotations and the formal names of organizations and events, other variations such as LGBTQIA are also acceptable with the other letters explained. I generally stands for intersex, and A can stand for asexual (a person who doesn’t experience sexual attraction), ally (some activists decry this use of the abbreviation for a person who is not LGBTQ+ but who actively supports LGBTQ+ communities) or both. Use of LGBTQ+ is best as an adjective and an umbrella term: Walters joined the LGBTQ+ business association. Avoid it to describe individuals or, for instance, if the group you’re referring to is limited to bisexuals. Queer is often used as an umbrella term covering people who are not heterosexual or cisgender and is acceptable for people and organizations that use the term to identify themselves. Do not use it when intended as a slur. Follow guidelines for obscenities, profanities, vulgarities as appropriate. See sexual orientation; gender identity.

Here's the entry: 

FAQ  Acceptable in all uses for frequently asked questions.

The first option. We capitalize titles only when they directly precede a name. Not after a name or when standing alone, as in your examples.

Yes, the reasoning outlined in that question/request describes the thinking behind our conclusion. We used the guidance in the historical periods and events entry and decided that this specific movement met that criteria. We did previously defer to Webster's New World College Dictionary, whose preferred style is lowercase. However, that dictionary also notes the frequent usage of the capitalized version. And Merriam-Webster uses the capitalized approach.

Correct on both counts. 

Yes, a comma after 2021. Also: In AP style, we abbreviate most months when used with a date. So our style is: between Feb. 1, 2021, and Feb. 22, 2023, the ...

Don't include the year if it's the current year. Here's the entry:

When a phrase refers to a month and day within the current year, do not include the year: The hearing is scheduled for June 26. If the reference is to a past or future year, include the year and set it off with commas: Feb. 14, 2025, is the target date. Use an s without an apostrophe to indicate spans of decades or centuries: the 1890s, the 1800s.

Years are an exception to the general rule in numerals that a figure is not used to start a sentence: 2013 was a very good year.

No of. Just March 2020. We may not have an explicit entry on that point, but an example is below (January 2016).

Capitalize the names of months in all uses. When a month is used with a specific date, abbreviate only Jan., Feb., Aug., Sept., Oct., Nov. and Dec. Spell out when using alone, or with a year alone.

When a phrase lists only a month and a year, do not separate the year with commas. When a phrase refers to a month, day and year, set off the year with commas.

EXAMPLES: January 2016 was a cold month. Jan. 2 was the coldest day of the month. His birthday is May 8. Feb. 14, 2013, was the target date. She testified that it was Friday, Dec. 3, when the crash occurred.

In tabular material, use these three-letter forms without a period: Jan, Feb, Mar, Apr, May, Jun, Jul, Aug, Sep, Oct, Nov, Dec.

See dates and years.

Correct, no :00 in our style. See the examples here:

Use figures except for noon and midnight. Use a colon to separate hours from minutes: 11 a.m., 1 p.m., 3:30 p.m., 9-11 a.m., 9 a.m. to 5 p.m.

Avoid such redundancies as 10 a.m. this morning, 10 p.m. tonight or 10 p.m. Monday night. Use 10 a.m. or 10 p.m. Monday, etc., as required by the norms in time element.

The construction 4 o'clock is acceptable, but time listings with a.m. or p.m. are preferred.

Yes: Season 1, Episode 8. (And if you can think of a better term than "sequential designations," let me know!)

The six-month investigation. Or, the 6-month-old investigation. Confusing, I know.

Arguments abound on each side of this question. A good general rule: If it's preceded by the, use the singular because the emphasis is on the number: The number of deaths has increased. But if it's preceded by a, use the plural: A number of deaths have been attributed to COVID-19.

You can consider anything and everything as one singular concept (though it's certainly lots of diverse stuff). So, anything and everything gets dumped here.

Take out Doris, and how would you say it? That's your answer (once you add Doris back in).

I am going to the store. Doris and I are going to the store.
The presents are for me. The presents are for Doris and me.

No hyphen. It wouldn't add any clarity. Thus there's no need for it. Now I will get some chocolate chip ice cream to follow my grilled cheese sandwich. Or maybe a peanut butter and jelly sandwich (please, no multiple hyphens in that one). And of course, our style says PB&J is perfectly fine. 

We do hyphenate three-word compound adjectives. We generally don't hyphenate ultra compounds:

ultra-  The rules in prefixes apply, but in general, no hyphen.

BUT bending the "rules" makes sense when a particular combination really doesn't work. And I'd say ultrahigh-strength really doesn't work.

So, I'd go with ultra-high-strength as the modifier. (Whatever ultra-high-strength means ... but that's another issue/question.)

FYI, this from 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. Consider carefully, though, before deciding to use more than three modifiers.

The hyphen is optional, as it is in many questions of compound modifiers. Interestingly, Webster's New World College Dictionary uses the hyphen for the modifier; Merriam-Webster uses no hyphen. Either is correct; it's just a matter of which you prefer. 

I think the phrase is well known and clear without the hyphen. 

We much prefer chocolate. For the sugary treat that you're asking about, Webster's New World College Dictionary prefers the two-word version:

jelly bean  a small, bean-shaped candy with a soft, jellylike center and a hard sugar coating: also written jellybean n.

Our style is PFAS for both the singular and plural. Here's the entry.

I'm curious, too, and I don't have the answer. That one has been in the book since well before my time. I don't know what led to the decision.

Both Webster's New World College Dictionary and Merriam-Webster hyphenate flu-like. But both also note that some -like words are hyphenated and others aren't, and that's a bit different from what the Stylebook recommends.  Perhaps a previous Stylebook editor was trying to bring some consistency to the equation. (That was my goal, too, once upon a time. Then I discovered it was impossible ...)

You certainly can use advisor if you prefer! Many people and organizations differ from AP style on one or many points. That's just fine with us.

We do have a style: stand-alone. We could drop it from the Stylebook, but deferring to Webster's New World College Dictionary (or for that matter, to Merriam-Webster, which is totally separate) would still result in stand-alone. There's no good reason to change simply because I (and other editors) tend to forget that particular rule. Since 2020, I have committed to always remembering this one.

All that said, I see in Google Trends that general usage strongly favors standalone. So does the American Heritage Dictionary. So there's that to consider. 

On the other hand, any time we change anything, there is outcry in the land.

Such is the Stylebook world. So many things to consider ...