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"But hey who cares about the story, let's just retcon a few more things like we did with Aidan and his brother, oh and bring old names like we did with Skeleton King and The Butcher, let's do that to our new expansion and enforce even more nostalgia. That totally worked with D3, let's do this again."
Also, inb4 Crusader is in fact a Horadrim.
If you're curious about recent Diablo lore and are legitimately interested in the answers to the questions you seek, I would highly recommend you check out some of our recent literary offerings, especially The Order, Sword of Justice, and the upcoming Diablo III: Book of Tyrael. Many of your questions will be answered there, though there is certainly more to come.

Just an FYI, keep in mind that the Horadrim were not a nation or civilization: They were an order of mages/warriors from all over Sanctuary. Cain was the last member of the PRE-EXISTING Horadrim Order. An Order does not go away unless it is completely and officially disbanded. Therefore, there cannot technically be the last of anything unless Cain was quite literally the only Horadrim left following the dissolution of the Horadrim Order (Which did not happen, the Order in and of itself still existed/exists, it was just down to one member)
You're very close. When Cain died, the Horadric Order did indeed die with his passing, but there's more!
In the continuing story revealed in Storm of Light and the events of Reaper of Souls, we find out that after the events of Diablo III, Tyrael himself revived the Order in order to help him safeguard Sanctuary and deal with the Black Soulstone.

So the Black Soulstone was stolen from Heaven? And Tyrael lost it almost instantly. Oh Tyrael, Imperius will devastate you this time
Well Tyrael didn't have a good option for the Black Soulstone. Since it's a man-made construct, he didn't know if he could destroy it, so he opted to hide it somewhere far away from both angels and demons.

Unfortunately, it didn't stay hidden for long.

After aiding in the battle against the new Prime Evil, i'd assume Tyrael would be able to call in a few recruits. And before you pull the 'but only the nephalem was at the battle', remember that there's also Bastion's Keep, where you were congratulated by every other person you saw.
Plus, it's easy seeing these new Horadrim guys aren't exactly masters at combat. They barely last 7 seconds.
To be fair, the Horadrim shown in the Reaper of Souls cinematic trailer were brave enough to stand against Death himself, and at least one got away in time to carry out Tyrael's message.

Tyrael wanted good but it came out as always
But to be serious, it won't probably be explained in the game so you could tell us now Vaeflare, How did Malthael found the hiding location? does he have allied Angels that are helping him or was he in disguise while spying on Tyrael?
That's a question I can't really answer here, but you may very well find the answers you seek in time within Reaper of Souls.

Why is it that Tyrael didn't think of destroying the Black Soulstone on the Hell Forge?
I'm sure he considered a lot of options, but the thing is, because the Black Soulstone is different than the soulstones of the past (like Mephisto's), and because it's a man-made construct, Tyrael wasn't sure what would happen if he tried to destroy it. Who knows what might happen if he attempted to do so? No one knows and such an attempt could prove to be catastrophic.

Therefore, he felt that the best and safest course of action was to keep the Great Evils locked within the Black Soulstone, and then hide it away from the influence of both angels and demons.

Now there are other dimensions that angels and demons created with the Worldstone, certainly. They're not really the sorts of places you'd want to go on vacation, though. Most of them are rather sad, empty places, and they are still the realms of the angelic or demonic faction that created that particular dimension.

The only truly neutral dimensions are Sanctuary and Pandemonium, but Pandemonium still has demons and angels in it, and Tyrael's mortal allies (the new Horadrim) wouldn't have been able to help him hide or guard the Black Soulstone in Pandemonium. As such, Tyrael believed that hiding it on Sanctuary was the best course of action out of the limited options available to him.

It would be kinda cool if you put the lore of the game IN THE GAME.
It's in there, and you can totally enjoy Reaper of Souls without having read the book.

Keep in mind that much of the basic lore discussion here surrounds a book that hasn't been released yet, as well as an expansion that hasn't been released yet, so you're due to find out more by playing the game once it's out, and/or by reading the book (if that's your thing).

Didn't anyone notice that in the RoS trailer, during the sketched animation near the beginning where it shows the black stone on the ground and the angels are surrounding it. I counted 4 angels. And since tyrael is mortal, that makes me think that the one high up above them all could be malthael.
Malthael isn't seen in that particular scene, but that's Itherael on the left and Imperius on the right.

Ever wonder what Nephalem are really thinking as they loot and plunder their way across the wilds of Sanctuary? Team Coco sought to answer this question in last night's episode of Conan on TBS.
Check it out!


(Who knew New Tristram was such a great place to go antiquing?)