Does Greyhawk exist in D&D 5e?

Does Greyhawk exist in Dungeons&Dragons 5 edition? How does the history of Tenser, Mordenkainen and Bigby (& their related spells) relate to #ForgottenRealms?

How does Savage attack and Brutal critical differ between greataxe and greatsword?

If cutting words is used on an AoE effect like fireball, does it reduce the damage?

If Mage Armor doesn’t count as armor then would a Monk get AC 13+Dex+Wis?

Counterspell & Dispel Magic : I know or I don’t know the spell’s level of the opponent spellcaster?

When the monster Manual list a specific save do you add that to the monster’s stat bonus?

Does balor’s Death Throes apply only when it dies in the Abyss?