"Chaos Emperor Dragon - Envoy of the End" sends itself to the Graveyard as part of its effect, and counts itself for determining how much damage it inflicts.
The damage that
"Chaos Emperor Dragon - Envoy of the End" inflicts is equal to the number of cards BOTH players send to the Graveyard times 300 points.
"Barrel Behind the Door" and
"Trap of Board Eraser" can be chained to
"Chaos Emperor Dragon - Envoy of the End"'s effect.
"Barrel Behind the Door" is, itself, sent to the Graveyard by
"Chaos Emperor Dragon - Envoy of the End"'s effect and counts for an additional 300 points as a result.
If
"Chaos Emperor Dragon - Envoy of the End" is destroyed or removed from play by an effect chained to its own effect, its effect still resolves.
Tokens will be removed from the field by
"Chaos Emperor Dragon - Envoy of the End"'s effect, but will not add to the damage total because they are not sent to the Graveyard.
It is the controller, not the owner, of
"Chaos Emperor Dragon - Envoy of the End" that can activate its effect and that inflicts damage to his/her opponent.
If you control your opponent's
"Chaos Emperor Dragon - Envoy of the End" and you pay the 1000 Life Points, the effect inflicts damage to your opponent even though the monster returns to your opponent's Graveyard.
If
"Chaos Emperor Dragon - Envoy of the End" is Special Summoned, and the controller immediately activates its effect, and the opponent chains
"Torrential Tribute" as Step 2 of a chain,
"Torrential Tribute" destroys all monsters on the field and sends them to the Graveyard, then
"Chaos Emperor Dragon - Envoy of the End"'s effect resolves, sends all Spell & Trap Cards on the field to the Graveyard, and inflicts 300 points of damage to the opponent for each Spell & Trap Card sent to the Graveyard by its effect. (Monster Cards do not count toward the damage because they were destroyed and sent to the Graveyard in the middle of the chain by
"Torrential Tribute".)
If
"Waboku" is chained to the effect of
"Chaos Emperor Dragon - Envoy of the End", it will not prevent the damage because
"Waboku" only applies to Battle Damage. Also,
"Waboku" will still be on the field when
"Chaos Emperor Dragon - Envoy of the End"'s effect is applied, so it will still count for 300 points of damage to the opponent.
When
"Minar" and
"Electric Snake" are sent to the Graveyard by
"Chaos Emperor Dragon - Envoy of the End", their effects are not activated because the modified text on those cards says when they are
"discarded to the Graveyard from the hand".