Would real Moody have taught 4th year students about Unforgiveable curses the way fake Barty Crouch Moody did?
In other words, did Barty teach about them (leaving aside his hands-on teaching approach) just to satisfy his Death Eater wishes, or did he teach them as part of his cover as Moody impersonator because Moody would have taught about them?
I'd say it's probably a combination of the two, though mostly part of his cover. Barty Crouch, Jr. likely wouldn't have passed up the opportunity to use the Unforgivable curses, but it also doesn't seem out of character for the real Mad-Eye Moody to give a practical demonstration to fourth year students.
"... I’m not supposed to show you what illegal Dark curses look like until you’re in the sixth year. You’re not supposed to be old enough to deal with it till then. But Professor Dumbledore’s got a higher opinion of your nerves, he reckons you can cope, and I say, the sooner you know what you’re up against, the better. ..."
Assuming that we can take the statement that it was approved by Dumbledore as the truth - and I see no reason why we can't, it would be very difficult to keep performing the Unforgiveables in front of students secret from the other teachers - then it seems that it was indeed part of the cover.
Crouch's job was to disguise himself as Moody and make sure that Harry won the Triwizard Cup, so he's not going to push heavily in favour of something that wouldn't be considered normal for Moody because it would raise questions. I suppose the beauty of impersonating Moody, as opposed to anybody else, is that he's viewed as pretty unstable by a lot of people anyway. Any slightly questionable actions - such as turning Draco Malfoy into a bouncing ferret - aren't going to make anybody suspicious.
I'm not supposed to show you what illegal Dark curses look like until you're in the sixth year. You're not supposed to be old enough to deal with it till then. But Professor Dumbledore's got a higher opinion of your nerves, he reckons you can cope, and I say, the sooner you know what you're up against, the better...
It seems like the curriculum for fourth year students does not include the Unforgivable curses. However Barty Eyed Mad Moody Crouch says that he received special permission from Dumbledore to teach them to fourth years. It is very unlikely that he lied about getting permission, as the students would undoubtedly be talking about the lesson outside of class, and he would not want to risk being found out so early in the year over something seemingly trivial.
Mad-Eye Moody may have done the same, though from the interactions that Harry has with him in later books, he seems like a by the books, strict, no nonsense individual. It would be impossible to know how he would have taught them however, and unfortunately we can no longer ask him.
However, teaching the lesson to the fourth year students definitely helped along Barty Crouch Jr.'s plans, so I think it is very likely that the lesson was part of the overall Death Eater plot that he had schemed. Though to be fair, it likely also helped out his cover since the motivation for Mad-Eye's actions to most people seemed dubious at best.
After the lesson, Neville is visibly shaken from the experience and is consoled by Barty and given the book, Magical Water Plants of the Mediterranean that Barty Crouch Jr. had hoped would help Harry get through the second challenge. It is possible that Barty needed an excuse to be overly generous to Neville, and used the lesson to upset him so much that he needed consoling. Barty Crouch Jr. was one of the Death Eaters responsible for torturing Neville's parents into insanity with the Cruciatus curse, so he would be well aware that performing it in front of Neville would likely elicit the response he was looking for.
That's a tricky one. Moody was fanatical when it came to his hatred of dark wizards, but he does also strike me as someone who would try to make his students aware of the stakes, and make sure that they were prepared.
I don't know about using the curses on students, but I could see him showing them the curses. That seems completely feasible. You have to remember, Barty was supposed to be as convincing as possible, so it seems likely that even if the real Moody wouldn't do that, his reputation and/or his personality made people who knew him believe he was capable of it. In fact, if Barty had thought it would arouse suspicion by using the curses, he would never have used them.
I could also see him comforting Neville, and probably being even more of a mentor to him than the fake was. As an auror and a member of the Order of the Phoenix, Moody would have felt a sense of camaraderie with the Longbottom family (he even talks about them when showing Harry the picture of the original Order). He might have even felt he owed them to teach Neville to defend himself and that Neville had a right to be able to take revenge. With his background, Neville might have been one of the only people Moody felt he could trust.
He might even have seen Neville as someone who would hate dark wizards as much as Moody himself, if not more, and could want to train him to be a sort of successor.
To be entirely fair, we like to make antagonists completely evil. Barty might have had a little good left in him when he took Neville under his wing. Barty hated death eaters who were never punished, and his father for not protecting him, but he had no real problem with Neville. He might even have felt a little guilty about what he did to the Longbottoms, even if giving Neville that book was intended to give Harry a clue.
His devotion to Voldemort may have been because of his long imprisonment in Azkaban, then at his father's hands. Voldemort freed him from prison, but when he was sent to trial, he didn't show any of his later fanatic devotion, even denying that he had anything to do with the Death Eaters. It may simply have been loyalty. As for the Longbottoms, I always got the impression that it was a random senseless act of violence brought on by poor decisions by Bellatrix than a planned move directed by Voldemort.
Barty praises Harry several times, and he might actually have liked him as a person, as he never personally seemed to hold a grudge. He only wanted to kill Harry out of his devotion to Voldemort. It might be possible he genuinely enjoyed teaching and actually cared a little for his students, so long as they were not obstacles to his master.
Well, yes, he does mention Dumbledore's permission, but I'm sure he was referring to be able to cope with things out of the fourth year curriculum, rather than Unforgivable Curses.
I feel fake Moody taught them Unforgivable Curses hoping that Harry might use it on his opponents, and it would be creepy for him to call Harry and show him some dead, tortured and Imperioused spiders.
