grammatical number - Singular or plural pronoun for an antecedent of the form "A, B, or C"?

The number, gender, and person of a pronoun must match its closest antecedent. Most style manuals advise using a singular possessive pronoun when the antecedent is a disjunctive set of singular nouns:

Either FDR, Churchill, or Stalin forgot to tie his shoes before the conference.

This makes sense because the pronoun refers to any one of the three nouns.

Meanwhile, a plural pronoun is appropriate when the antecedent is a group of singular nouns joined by a conjunction:

Churchill, Stalin, and FDR attended the conference but forgot to record minutes of their deliberations.

Again, this makes sense because the pronoun must refer to all three nouns.

Question: Is a singular possessive pronoun still appropriate when the antecedent is several nouns joined with "or" but the pronoun must refer to all the nouns at once? Here is an example:

Churchill, Stalin, or FDR or one of their male staff members dressed as a woman. The KGB found a dress in the shared laundry hopper.

Using "his" as the possessive pronoun just doesn't sound right in that sentence. Is that because the pronoun is really referring to the group of Churchill, Stalin and FDR? Parenthesis help illustrate:

(Churchill, Stalin, or FDR) or (one of their staff members) dressed as a woman. The KGB found a dress in the shared laundry hopper.

continuity - How do the Dallas movies fit between the old and new shows?

The two movies are ignored in the continuity of the show.

Cynthia Cidre, the new show's writer and executive producer, addressed this in an interview:

Interviewer: In JR Returns the scene was set for a continuation of the Barnes Ewing
feud. Why did you move away from this?

Cynthia - I was told, not necessarily to pick up where it left off but
not to pay to much attention to the movies because the movies had
tried to wrap stuff up in two hours. But we did not, I have to admit,
although I saw one of them, I did not download it in my brain. I was
really going off the end of the season, I don't pick it up from then,
its now 2012 so we have not seen the Ewing family in all those years
but now we are going to see them and they look good.

Therefore, the two movies were not considered canon. This can be seen in the treatment of JR. For example, in the first film it was revealed J.R. shot a mirror and left to go to Europe. In the second film, he returned and tried to regain his empire. All of this is ignored in the new series.

So the two Dallas movies have officially been retconned and are no longer canon.

What is the students' jargon or abbreviation for assignments made up of "only" data downloaded from the internet in English? (If it exists)

Japanese students call a report and essay made up by only putting data downloaded from the Internet e.g. passages from Wikipedia put together without including their own thoughts or creative ideas, a “コピペ-Kopipe,” which is pronounced as 'kopipay.'

It is a compound of ‘copied + pasted + paper’. Incidentally ‘copy ,’ ‘paste,’ and ‘paper’ are all adapted to Japanese language, and pronounced as ‘kopi-i, ‘paisuto, and ‘paypah’.

To me 'Kopipe' is akin to plagiarism, but it doesn’t have the same criminal overtone as plagiarism itself. It seems to be just a labor-saving editing or blending job for students.

While riding on the train, I've overheard students say to each other:

“I submitted a report in time by ‘kopipeing’ articles”

innocently, as if they were playing a game.

Is there a similar student jargon or abbreviation for ‘Kopipe’ in English?

punctuation - Should there be a period after an equation?

I don't know if LaTeX is considered a definitive source for mathematics writing style (although it was developed for typesetting math equations), but this link and this one seem to indicate that, yes, a period would be inserted after the equation in the example

We used the equation

x + y = z.

This is the next sentence.

The Wikipedia Manual of Style (Mathematics), which cites several published mathematics style guides, offers this wisdom (emphasis added by me):

Just as in mathematics publications, a sentence which ends with a formula must have a period at the end of the formula. This equally applies to displayed formulae (that is, formulae that take up a line by themselves). Similarly, if the conventional punctuation rules would require a question mark, comma, semicolon, or other punctuation at that place, the formula must have that punctuation at the end.

The reference for this section is Higham, Nicholas J. (1998), Handbook of Writing for the Mathematical Sciences (second ed.), SIAM, ISBN 0-89871-420-6. The notation states that this is the style adopted by "many mathematics journals," so it is probably a safe choice.

Alternatively, you could use

We used Equation 1.

Equation 1.

x + y = z

This is the next sentence.

B grade 80's movie about a commando hunted like an animal

I'm pretty sure your thinking of Deadly Prey from 1986. The plot, as taken from Wikipedia is

Colonel Hogan rents his mercenaries out to anyone with the right
price. This time it's businessman Michaelson. A deal is struck, and
Hogan recruits new troops. For training, he orders his troops to
kidnap innocent people, take them to the forest and hunt them.
Unfortunately this time, they picked the wrong guy, Mike Danton.
Danton, a Vietnam veteran, is ambushed while taking out the trash.
Taken to the forest, he is stripped to his shorts, greased up and told
to run. The mercenaries hunt Danton, but are meticulously picked off
one by one. The troops report this to Colonel Hogan, who sends a task
force with his best man, Lieutenant Thornton. One of this elite combat
unit is Jack Cooper. Cooper and Danton realize who each other are
while trying to kill each other. Cooper has not seen Danton since he
took a bullet for him in 'Nam. With his new-found friend, Danton
continues to punish the mercenaries, and get back to his wife Jaimey.
Like all good villains, Hogan uses Danton's family against him, but
this angers Danton. After storming the military training camp Danton
arms himself up, and destroys all traces of Hogan's mercenaries.

There is an extended trailer on YouTube here. At the 5:50 mark you can see the scene where Denton cuts of the guys arm and beats him with it.

the hobbit - Why wasn't Sauron invisible when he wore the Ring?

Usage of the rings of power are based on the experience/desires of the user as well as the limitations of the ring itself. In The Hobbit, when Bilbo first used the ring (in Gollum's lair) his greatest desire at the moment was to go unnoticed (i.e., invisibility). Frodo likely had the same experience since his initial understanding of the Ring was as limited as Bilbo's. Keep in mind that in the LOTR books, another character, Tom Bombadil also did not become invisible (or affected in any way) when wearing the ring likely due to his experience as a much older magical being. Thus, Sauron could use it to help create entire armies, whereas magically inexperienced Hobbits simply became invisible.

Also, what Oliver_C answered.

a song of ice and fire - In Game of Thrones season 2, why do they (possible spoilers)?

This was something that was changed from the book. My answer will be based on the book A Clash of Kings.

Initially Qhorin states that it will be easier for Jon if the rest do not watch.

“Then you must do what needs be done,” Qhorin Halfhand said. “You are the blood of Winterfell and a man of the Night’s Watch.” He looked at the others. “Come, brothers. Leave him to it. It will go easier for him if we do not watch.”

However it is later revealed that Qhorin didn't need her dead, he just
wanted to test whether Jon would kill her.

Qhorin’s shrewd grey eyes seemed to see right through him. “So you let her go?” He did not sound the least surprised.

“You know?”

“Now. Tell me why you spared her.”

It was hard to put into words. “My father never used a headsman. He
said he owed it to men he killed to look into their eyes and hear
their last words. And when I looked into Ygritte’s eyes, I...” Jon
stared down at his hands helplessly. “I know she was an enemy, but
there was no evil in her.”

“No more than in the other two.”

“It was their lives or ours,” Jon said. “If they had seen us, if they
had sounded that horn...”

“The wildlings would hunt us down and slay us, true enough.”

“Stonesnake has the horn now, though, and we took Ygritte’s knife and
axe. She’s behind us, afoot, unarmed...”

“And not like to be a threat,” Qhorin agreed. “If I had needed her
dead, I would have left her with Ebben, or done the thing myself.”

“Then why did you command it of me?”

“I did not command it. I told you to do what needed to be done, and
left you to decide what that would be.” Qhorin stood and slid his
longsword back into its scabbard. “When I want a mountain scaled, I
call on Stonesnake. Should I need to put an arrow through the eye of
some foe across a windy battlefield, I summon Squire Dalbridge. Ebben
can make any man give up his secrets. To lead men you must know them,
Jon Snow. I know more of you now than I did this morning.”

“And if I had slain her?” asked Jon.

“She would be dead, and I would know you better than I had before. But enough talk. You ought be sleeping. We have leagues to go, and dangers to face. You will need your strength.”

I've bolded the important parts of the quote.