Blessings From Above

Don't bother with this one if you're going for Loremaster. It's a repeatable (even though it's a yellow exclamation mark) and will not count for Desolace Quests.

Ten Pounds of Flesh is the quest that counts for Desolace Quests.

This quest does not count. Ever. The first quest the Brazier gives you is a totally different quest. Both quests have the exact same objectives, but Blessings From Above is not the quest that you get when you first visit the Brazier.

SanderZammy is 100% correct and should not be downranked. Isshin is 100% incorrect and should be downranked.

This quest is a Repeatable quest.

Repeatable quests are quests that can be completed more than once. It's possible that any experience or reputation rewards are only rewarded the first time this quest is completed, but nevertheless, completing this quest will not make it appear as completed in the Wowhead quest tracker, and it can therefore be safely excluded if you're a completionist.

Examples of Repeatable quests:

• Buff quests.
  Most common example. You collect certain items that can be gathered even after completing the associated buff quest once. Turning them in may grant a buff. These quests are repeatable so that you can refresh the buff anytime, by completing the quest again.
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• Item quests.
  Uncommon. Quests that reward you an item which, for example, is required in another quest. Sometimes these quests are repeatable so that you can get more of these items if necessary.