Regarding Azalon, if I'm right, and the way to trigger the quest is to talk about "disappearances" with the prosttute, then that fact probably accounts for why you missed it. The topic "disappearances" also has to do with the missing people in the crypt and with Draest, and that's what most NPCs talk about when you ask them about disappearances.
Here's another update on my progress:
SPOILERS
Regarding the goblin quest, the one thing that for me really merits discussion (i.e. it is less than fairly obvious) is the maze and goblin treasury that is accessible from the goblin crypt. Exploration of the maze and treasury is related to the quest that you should have been given by the skeleton king standing on the outdoor stairs - he asks you to find his crown. Getting to the goblin crypt is fairly straightforward and should produce no difficulties. Finding the maze, however, can be tricky. In the top room of the crypt, (where you can find the door to the throne room), there is a secret passage that will lead you to the maze. The passage is to be found behind a secret door, located roughly in the center of the room, on the ground level. The door itself looks just like a piece of wall, but the description "secret door" will show up when you get close enough to it.
The maze is reminiscent of Eye of the Beholder - constricted, all right angles, narrow corridors etc. It is without a doubt one of the most fun dungeons I have played in Morrowind. The interesting feature here is that automap is blackened out. There is no need to map the maze, though - just follow the simple rule of keeping to the right (or left, as you prefer) wall at all times, make all turns to the right etc. and you will traverse the maze. I don't have mathematical proof of this, but it seemed to me that this maze was designed in such a way as to be traversible in its entirety by simply always following the wall to your right (or left, your choice). Two other things: (1) be thorough as you follow the wall - even if you can see that a passage dead-ends, check it anyway for a secret door, and (2) if you wish, use the note feature of your map (I found it helpful); to activate it, right-click to bring up the map, and then double-left-click on a spot on the map to write a personal note for that location. So, e.g., if you see a pair of chests across a grille that you can't get to yet, make a note of it - that way you get some reference points and you can be sure that you didn't miss the chest. Notes are editable and deletable.
As you wander in the maze you will eventually encounter a door to the secret goblin treasury. If you have good enough lock picking skills, you should have no problem opening the chests and also reaching the altar where the skeleton king's crown can be found. Word of advice - have some means of high jumping or levitating available. Returning the crown to the king is something that gave me trouble - the first time around, I couldn't leave the goblin castle, but after I saved and reloaded, I could step outside again and give the crown back. The reward for this is the key that supposedly opens the chests in the treasury - I never verified this, because I had good enough lock picking to not need a key.
As an aside, the ability to write your own notes onto the map will also come in handy in some of the goblin caves levels, where your map is blacked out or where you have to deal with teleporters and want to record which teleporter takes you where etc.