Tabitha Heartweaver - Silverpine Forest, 44.5, 43.0. As you enter the Sepulcher, she is standing by the graves on the left side. You must be level 15 to accept this quest and there are no pre-requisites.
How to complete the quest
This quest asks you to find Edward Heartweaver.
After defeating the last boss Rath'mael, clear the pack of Ghouls to the left as you enter the boss arena. There you will find an Undead NPC on the floor - walk over to him to complete the quest. If you are struggling to find him you can type /tar Edward Heartweaver, right click the profile, and apply a target marker.
Crest of Lordaeron
Where to start the quest
The Crest of Lordaeron is an interactable item found within the dungeon. Find the item to start the quest. You must be level 15 to start this quest.
How to complete the quest
The Crest has various different spawn locations within the dungeon
As you enter the dungeon, turn right. There is a tower with a climbable staircase - the Crest can spawn up the top of the tower.
Again turning right from the entrance of the dungeon, in the south-east of the map is an interactable door that when opened spawns a hostile Banshee. The Crest can be found behind this door.
There is a tower by The Abandoned boss. Like the first, climb it to potentially find the Crest.
In the Bjork boss area, there is an entrance to an otherwise empty room. The Crest may sit at the foot of the stairs here.
Again near Bjork, head north-west to the pavillon. The Crest may be sitting on a wall there.
Light's Justice
Where to start the quest
Morbin Lightbane - Undercity, 58.0, 90.0. Located in the room with Sylvanas and Varimathras. You must be level 15 to accept this quest.
How to complete the quest
This quest asks you to collect 25 Intact Limbs.
Skeletons and Ghouls are the main drop sources for these Limbs. They are located all throughout the dungeon, specifically towards the south and west, and are plentiful enough that your whole group should be able to find enough in one run. You may need to clear extra packs to find enough.
The New Plague
Where to start the quest
Apothecary Renferrel - Silverpine Forest, 43.0, 41.0. Towards the right-hand side of the inn entrance in the Sepulcher. This quest is part of a chain starting with A Recipe for Death, which asks you to collect various viscera from the mobs in the area.
There are 3 quests to complete before being eligible for The New Plague, which is then picked up from Theodore Griffs in The Apothecarium, Undercity 46.0, 72.0. You must be level 15 to start this quest.
How to complete the quest
This quest asks you to collect a Highly Toxic Strain.
The item is looted from the Spider boss, Witherfang.
The Wrath of Rath'mael
Where to start the quest
Deathguard Linnea - Tirisfal Glades, 65.0, 60.0. As you exit Undercity, take a right down the path to find a small camp. The first quest in this chain is called Rear Guard Patrol, for which you'll need to kill a handful of undead in a farm to the east, and then a follow quest to dispatch of an elite abomination in the clearing just under Scarlet Monastery.
After completing these two quests, The Wrath of Rath'mael will become available from Deathguard Kristof located in the same camp. You must be level 15 to start this quest.
How to complete the quest
This quest asks you to kill Rath'Mael, the last boss in the dungeon.
Don't forget to fully explore this area to complete A Frightened Request.
Unending Torment
Where to start the quest
Loot the Abominable Head dropped from The Baron. You must be level 15 to start this quest.
How to complete the quest
Return the head to Master Apothecary Faranell in the Undercity 48.0, 69.0. You will have to complete a few more follow-up quests to unlock the quest's items.