Sunset Girl: You raise some interesting questions, and the best way I can think to reply is to offer a plausible timeline, based on events we know happened and knowledge of characters we know so far.
I think this is how it went down: Regulas got involved with the Death Eaters at a young age. I don't know if it was while he was still at Hogwarts or shortly thereafter. I also have no idea what his motive for doing so was. In the magical world, just like in the muggle world, there are few secrets. Think about how many people were SUPPOSED to know about the prophesy regarding the baby and Voldemort. Should have been just Dumbledore and Trelawny. But Snape overheard, and as a result, Voldemort found out (only Snape and Voldemort had only half of the prophesy, but it was enough to make them act on it). I think it's quite possible that that's how Regulas came to know about the necklace: overhearing something about it. Perhaps it wasn't even about the necklace at first, maybe it was just knowledge of Horcruxes, and he continued to do homework after that to pin down specifics. Regardless of how much he actually knew, I think the very idea of Voldemort making even one Horcrux could have shocked him into the realization that he was in too deep with a terrible, terrible, terrible man. Horcruxes aren't even written of in the darkest of dark books available, so that's the feeling he must have walked away with when he found out there was at least one Horcrux. For a short time, I think he was something of a freelance spy. He wasn't reporting to the Order, but he wasn't loyal to the Dark Lord, either. I think he may have known he couldn't continue, and maybe felt like there might be ONE thing he could do to sabatoge Voldemort's efforts before he met certain death for abandoning the Death Eaters, so he either used the information he overheard or he researched and was able to ruin the Horcrux in the cave. I don't know how long it was after that that he was killed, or if Voldemort had any idea at the time what he had done.
Your statement that if Regulas was a reluctant Death Eater, he wouldn't have had the bravery needed to do what R.A.B. (whoever he or she may be) did in the cave, is, I think, really mistaken. It is common sense, not a lack of bravery, that makes us fear very real threats. He would have had to be psychotic to not have a STRONG sense of fear regarding Voldemort after he gained knowledge of the Horcrux. That kind of fear is what makes us be careful in dangerous situations, and to do what he did would have required an enormous amount of bravery. He knew, beyond a shadow of a doubt, more than probably anyone else out there, just who he was dealing with, and he made a serious step to thwart Voldemort's efforts at immortality before facing the inevitable confrontation that would end his work with the Death Eaters, and that would end his life. To do what he did, with the knowledge that he had, makes him one of the bravest people in the books, even if it was at the very end of a career as a Death Eater.
Hagger: Was Aberforth a spy? Possibly.
What do we know?
1. He's Dumbledore's brother.
2. He did something inappropriate with a goat. (I'm dying of curiosity)
3. He was at one gathering of the Order.
I'm going to throw this in the mix:
4. We know of at least one instance of a Death Eater being in The Hog's Head (Snape on the night of Trelawny's prophesy), and we have further evidence that The Hog's Head attracts folks of a shadier nature.
What do we not know?
1. Exactly what he did with that goat (sorry. I'm going to be ticked off if the seventh book doesn't reveal that
)
2. Why he only made one appearance all those years ago with the Order.
3. Why he hasn't resurfaced as a member of the Order (that we know of) this time around.
4. What his duties were with the Order last time.
5. How old he would be.
6. Whether he's still alive or not.
7. What House he was in at Hogwarts.
I don't think he would have been the kind of spy who would ingratiate himself with the enemy for a few reasons. He would have to have the physical mark as proof of serving the Dark Lord, and he would have to behave like a Death Eater, performing Unforgivable Curses and all. Snape was able to do it since he already had the mark, and his past was dark. Not to mention, Snape could use the excuse that he couldn't very well go about cursing people left and right and not have it get back to Dumbledore, so he could get away with avoiding dark magic. I seriously doubt Dumbledore would condone the use of Unforgivable curses in order to fit in, so Aberforth couldn't very well try to join Voldemort, but avoid performing the evil curses. That would have been worse than extremely suspicious.
He could have been a spy in the eavesdropping kind of way, which is how I support my Hog's Head theory. That would be one MAJOR coincidence that Snape, a Death Eater, just happened to be in the Hog's Head and overhear the prophesy, if he (or other Death Eaters) don't go there often. Fast forward fifteen years, and you could very well have Snape ingratiated (even if he is double-crossing, to Dumbledore's mind, he's an inside spy, then Aberforth could be someone to eavesdrop ("Dung" has the same responsibility, apparently, because he told Dumbledore of the DA).
All this is assuming, of course, that Aberforth is still alive (which we really don't know) and that he's a loyal, active member of the Order (theoretically, I guess, he could have turned, or he could have decided not to be involved due to age or illness, since I don't think we know how old he is, or if he is Dumbledore's older or younger brother).
I don't see how in the world Aberforth could rise up as the new leader of the Order, though. The original members saw him once. The newer members haven't seen him involved at all. It's not like this is a monarchy, where the leader's next of kin would step in after the leader's death. The fact that Dumbledore and Aberforth are brothers doesn't mean that Dumbledore would have shared highly confidential information with him. I'm of the opinion (although it's just theory on my part) that Harry was the closest thing to a true confidant Dumbledore had. Dumbledore knew Harry would HAVE to have that information, but I always got the feeling that Dumbledore didn't confide in people, and he carried the weight of that knowledge with him.
One more thing. The comment about the alchemist job based upon the search for immortality doesn't seem quite right. The elixer of life did come to be because of the work of an alchamist (spelling anyone?) This may be strange, but I don't think they went to work on trying to come up with the elixer of life with the kind of passion that Voldemort showed searching for it. I once heard that Alexander Graham Bell came to hate his own invention of the telephone. I kind of wonder if this is how Dumbledore and Flamel came to feel about the Elixer. They came up with it, and quite possibly didn't have the foresight to know some truly evil wizard was willing to kill anyone in his way to gain immortal life, even if it meant killing others, even babies and children. I've also heard that immortality actually sounds more appealing to the young than the old, so it may be that Dumbledore developed his opinion of immortality and the positive side of death AFTER the discovery of the elixer. In theory, discovering the secret to immortality seems like a wonderful thing. But when you realize the complications it can cause, it becomes clear that it's a very very negative thing. (BTW, just like the Flamels, who continued to use the magic of the elixer, Mr. Bell didn't throw out his telephone
)
Without Dumbledore around, I think Harry's going to have to take charge of the Order. He has A LOT of work that he knows has to be done quickly, but almost all of it must be done by him (possibly with the help of Ron and Hermione). Therefore, I think the Order (and not the DA, but possibly the Order will accept the younger generation in, considering all that's happened) will have two main jobs. The first, naturally, is to protect Harry (which has been a major, if not THE major, purpose of the Order this time around) and the other is to prepare for war with Death Eaters, giants, and any other evil beings who are backing Voldemort up.
I think I mentioned once that when I'm tired, stressed, etc. I tend to ramble. Sorry.