Lowercased in that usage.

I think that's a judgment call. Certainly if you're quoting from a transcript or other written material, you would want the ellipses. On the other hand, it's common practice for reporters to use parts of quotes without ellipses and assuming that they don't distort the meaning, it's usually fine.

A key question is how to accurately convey the quote and the intended meaning to readers. If the two sections of the quote are separated by only a few words, or maybe a sentence that doesn't change the meaning, it may be fine to not use the ellipses. On the other hand, if there's lengthy and-or substantive material that's being left out, you'd be representing it better with the ellipses.

Consider: 

"We had tried a number of things to remedy the situation. Finally we decided that is the one that was most important."

vs.

"We had tried a number of things to remedy the situation. First we tore off the roof, then we gutted the kitchen, then we increased the budget by $40,000. It was much more of a nightmare than we ever envisioned. We were ready to give up. I mean, really, we were about to go bankrupt. Then we tried rerouting all of the electrical work, and out of all the solutions, that is the one that was most important."

Ellipses  or not?

Or, you could just paraphrase.

No, because it puts too much separation in thought from the time of the seminar and leaves unclear when it will occur on June 27. A comma would be better. 

There's a lot of detail in our privacy entry. Here are the key points:

Generally, we do not identify juveniles (under 18) who are accused of crimes or transmit images that would reveal their identity. However, regional editors or their designates may authorize exceptions to this practice.

Considerations in granting exceptions may include the severity of the alleged crime; whether police have formally released the juvenile's name; and whether the juvenile has been formally charged as an adult. Other considerations might include public safety, such as when the youth is the subject of a manhunt; or widespread publication of the juvenile suspect's name, making the identity de facto public knowledge.

In some situations, state or national laws may determine whether the person's name can be published.

I definitely wouldn't use quote marks, which are confusing and don't look like emphasis. Perhaps capital letters: I REALLY loved that movie. 

There are so many ways to have fun with this!

I see your concern about the original phrasing, which conceivably could be read as indicating three people. Logically, though, that three-person interpretation probably wouldn't happen in this case unless Theresa had already been referred to earlier. Otherwise she's just popping up out of nowhere, with no first reference.

But I'd hate to make a blanket statement that such a construction is OK in every case because there certainly could be times when confusion would result.

Option 1 is out of the question unless you have more than one wife and you are clarifying that Theresa is the one in question.
Option 2 is OK but the dashes are annoying. They make it look as if you are putting particular emphasis on her name.
Option 3 is OK, though we're not a fan of parentheses.

It's correct. I wouldn't put the quote mark around firsts, though. 

In this case, I'd use the numeral 3 to avoid looking odd to readers, who aren't up on the intricacies of AP style.

We don't use Dr. or any other title on second reference; just the last name. You could decide to deviate from our style, of course.

Yes.

Thanks for noting that; I see that indeed we have been inconsistent. The Stylebook team will address this. I don't have an answer right now. 

We don't hyphenate those combinations.

I'm not sure where you're seeing that. Could you point me to it? We do specify that state abbreviations should be used in most datelines, which are separate from the story text:

ABBREVIATIONS REQUIRED: Use the state abbreviations listed at the end of this section:

–In conjunction with the name of a city, town, village or military base in most datelines. See datelines for examples and exceptions for large cities.

I'll see if the Religion chapter can be hyperlinked. It might not be possible to link an entire chapter. But it does still exist. You can find it in the View by Chapter > Other Chapters dropdown box.

It's certainly fine to refer to a priest as Father in conversation or informal writing. The formal style is to use the title the Rev.

Now I can't get that image out of my head. Yet another example of fun with the language. The Stylebook's official dictionary, Webster's New World College Dictionary, also styles it pickup for all uses (at least, as many uses as the dictionary editors could think of). We defer to them on this matter. The full dictionary entry is below, for those interested in the many ways pickup can be used:

 (pik´up) n. 1 the act of picking up, as in fielding a rapidly rolling baseball 2 the process or power of increasing in speed; acceleration ☆3 a small, open truck with low sides, for hauling light loads: in full pickup truck 4 [Informal] a) the act of making the acquaintance of a stranger in a quick and flirtatious way with the hope of a romantic or sexual encounter b) a person with whom such an acquaintance is formed ☆5 [Informal] improvement or recovery, as in trade ☆6 [Informal] a) a stimulant; bracer b) stimulation 7 a) in an electric phonograph, a device that produces audio-frequency currents from the vibrations of a needle or stylus moving in a record groove b) the pivoted arm holding this device 8 a) the reception of sound or light for conversion into electrical energy in the transmitter b) the apparatus used for this c) any place outside a studio where a broadcast originates d) the electrical system connecting this place to the broadcasting station 9 a small microphone attached to a vibrating surface, as in an electric guitar –adj. [Informal] 1 assembled informally for a single engagement, contest, etc. [a pickup jazz band or baseball team] 2 of a game or job performed or played by those assembled in this way 3 designating a window at a restaurant where prepared food can be bought by customers in cars 

Much in English language and usage (and, I assume, other languages and usages) isn't entirely logical or consistent. In many cases, our style reflects how usage has evolved. Carmaker and automaker evolved in that style, as one word with no hyphen, and are listed that way in our official dictionary (Webster's New World College Dictionary). So we have adopted that style for those words. Same with policymaker, boilermaker, filmmaker, winemaker, among others. Other -maker creations haven't evolved that way. For those, we follow the style of our -maker entry and the version used by Webster's. Rest assured, when we figure out a way to make the language and usage entirely consistent both within one country and across many countries using versions of the same language, we'll update the Stylebook accordingly.

Really, it has to be rephrased. That's the only way to be clear to readers and not create some crazy punctuation just because the writer doesn't want to recast it.

The guidance remains the same; the entry itself has been moved to the internal AP section of the Stylebook.

It should be deal-making and deal-maker. Thanks for asking.

The way you have it works.

Yes, your interpretation is correct and so is your reasoning about this example. The phrase pain management is pretty common, and you can consider it a noun phrase with no need of hyphen. It's understood without a hyphen, and there's little chance of confusion without the hyphen. 

If possible, rewrite to: People in Georgia who find themselves in such a situation ...

AP style is to use parentheses, not brackets. If your newspaper prefers to use brackets, that's certainly a choice that you folks can make. 

It might depend on the context; I suppose there are some situations in which quotation marks would be appropriate. But it's a valid word on its own. Here's the dictionary entry:

 (-mənt) n.  1 the condition or state of being entitled 2 something to which a person is entitled; specif., any of various benefits provided to qualifying persons under certain government programs, as Medicare