Insert snappy preamble here.
"I have a question about the Draenei. Mainly, why have they stayed in Azeroth? I mean, I know for the sake of gameplay this is how things are, but is there any justification for it? Shouldn't Velen be in Shattrath?"
Like the Orcs, they've made Azeroth their home. Their original homeworld is prime Legion territory right now, and they can't go back there. Outland is in shambles for the moment. We purged the darkness of Outland (mostly) but it's still a mess. Azeroth is home to the foretold Army of the Light. The Draenei want to stick around. They like the place, and it's probably their best chance at a new beginning... and defeating the Legion. They want to stay close to other Light-following people. When your biggest enemy is the Burning Legion, why wouldn't you?
"I read the WoW book "Tides of Darkness" where the Horde first began to invade the eastern kingdoms and the book went into the Alliance's creation of Paladins. Basically, they were originally Priests who learned to fight more like a Warrior while retaining their faith. This to me seemed like a logical conclusion since in times of battle, it helps to be able to physically defend yourself. My question is, why have night elves, trolls and undead not come to this same logical conclusion? I mean, each of these 3 races already are aligned with a race who knows how to transition from Priest to Paladin (blood elves for the horde and various races for the alliance), why hasn't someone told them how to do it?"
On a large scale, taking an overhead look of the entire race, Trolls, Night Elves, and to a much lesser extent the Forsaken, may not have the capacity to become Paladins, or even the interest in it. Remember, Night Elves and Trolls have Priests, but they do not follow the same faith that the current living Paladins do. Night Elves draw their power from Elune, not the Light. Can Elune have Paladins? Would a Paladin of Elune have the same capabilities, or would they be different? The same goes for Trolls. They're more like friendly Witch Doctors. The abilities all have the same names for ease of use in-game, but Blizzard has made it clear that they do not all share the same faith.
In the case of Night Elves, their Paladin equivalent would probably be the Priestess of the Moon, which is the class role Tyrande filled in Warcraft III, and their capabilities are elaborated upon in the War of the Ancients trilogy. They wear plate over their cloth, much like Paladins. However, there are some huge differences. They draw their power from the Moon, not the Light. They, like most warriors in Night Elf culture, prefer to attack from range, using bows and arrows. The class 'progression' exists in other cultures, it just doesn't necessarily sync up with Priest to Paladin.
Taking a closer look at the races, taking individual cases into account, sure, there could definitely be Paladins of those races. One point Blizzard has made about the Light is that it doesn't discriminate based on race. Even the little bit about the Forsaken being burnt to a crisp by the Light due to their undead nature has been lifted over the last few years. The Light does not at all discriminate. Night Elves and Trolls can worship the Light rather than their native gods and goddesses if they want, but will that happen? Not very often. The Forsaken can continue to worship the Light as they did in life, but most of them have turned primarily to the Shadow aspects of the Light. Paladins absolutely can exist in this races, but they are going to be incredibly rare.
If you want to see Paladins of unusual races, just hang out with the Argent Crusade. Most of the Argent Crusade is Humans, but there are Trolls and Night Elves scattered about that are wearing plate armor and have mana bars. They're not specifically stated as being Paladins, but it's a safe assumption. Paladinhood aside, there are still examples of some of these races following the Light, so it's possible. Zabra Hexx, who was a character in the Ashbringer comic, is a Darkspear Troll that found the Light. Chancellor Velora is the subject of a TCG card and as an Undead Priestess, her flavor text says: "The Light rewards faith, not form."
It's absolutely possible that these races can have Paladins. However, you wouldn't see one every day, and that's why they aren't playable. The playable classes are the aspects of the races that you would encounter every single day walking through town.
"Why can't Forsaken be of any race (and therefore of any class)?"
This is a one part lore, one part game mechanics answer. As far as lore goes, most of the Undead are humans, citizens of Lordaeron. There are other races that've been risen, but they're few and far between compared to the Humans since it was Lordaeron that was struck by the Scourge, not Orgrimmar or Ironforge or whatever. Classes are always based on what you're most likely to see in a specific race. It's the same for the Forsaken models.
Now, game mechanics. It would be really cool to have a Tauren Forsaken, but is it a Tauren of a Forsaken? What racials does it have? Could you, at a glance, tell whether that character off in the distance is a Forsaken or a Tauren? Even worse, what if it's a Dwarf? Could an Alliance player tell that that's a Forsaken Dwarf off in the distance and not a Dwarf Dwarf? Would they be able to easily tell the difference if one ran up behind them in PvP? Those are all problems in a game like this, the races need a distinct look. The Forsaken have one consistent appearance all of their own, and mixing that up any further makes them more difficult to recognize, which isn't a good thing at all in a game like WoW.
"The future expansions will involve the Emerald Dream and/or the Maelstrom, but what races/classes are likely going to be implemented. Goblins for Horde? Furbolgs for Alliance? Demon Hunters? I'd just like to hear your thoughts on this."
If you want my personal, honest thoughts on the matter, I don't think we'll see any new races or classes in the next expansion. Even if it turns out to not be the Maelstrom, my answer is the same. I'll be very pleased if Blizzard proves me wrong, but I don't think we're going to see any at all.