No, it becomes an Equip Card on resolution. While it is not initially a continuous-type card, it will act as one when it turns into an Equip, and will remain on the field until destroyed, or it becomes unequipped (which will destroy it too).
No, 'Metalmorph' does not get sent to the graveyard at the end phase. It is a Continuous Trap Card and will remain on the field until it is removed by a card effect or destroyed by battle.
Egyptian God cards can be Special Summoned from the Graveyard. However, their card effect states that, "When this card is Special Summoned, it is sent to the Graveyard during the End Phase" (according to the Yu-Gi-Oh! World Championship 2009 versions).
No and yes. After it attacks or is attacked, the Gladiator Beast monster must survive the Damage Step to be able to return to the Deck at the end of the Battle Phase. If it is destroyed by battle, it is sent to the Graveyard, and cannot activate at the end of the Battle Phase.
Yes. Whether the cards are sent as a cost to activate an effect, or on resolution of their end phase triggers, any monster card sent from deck to graveyard by a Lightsworn will cause damage to be dealt by Coffin Seller.
No. A discard is a special kind of 'send'. All discards are sends, but not all 'send from hand to graveyard' are discards. This kind of send will only be considered a discard if the effect specifically says it is a discard. Also cards are 'discarded' in the end phase if you have more than six in hand and wish to end the turn.
No. If the effect didn't say it was a discard, then it is not a discard. The only exception is for cards sent to the graveyard in the End Phase if you have more than six in hand. These are discards.
Any movement of a card from another zone to the graveyard, is a send. 'Tribute', 'Discard' and 'Destroy' are specific kinds of send. XYZ material is 'sent to the graveyard' if the XYZ monster that overlays them is destroyed, removed from play, returned to the Extra Deck, etc.One exception is cards that have been removed from the game. They can be 'returned' to the graveyard, but not 'sent' from there.
Horus Lv6 says, that at the End Phase of the turn in which it destroys a monster by battle, that you can send it to the graveyard to special summon Lv8. This means Horus Lv6 must still be on the field after the battle phase, all the way to the end phase. If it gets destroyed during the battle phase, then it cannot summon Lv8.
Odin says that if he is destroyed, you may resummon him by removing a Tuner from your graveyard, during that turn's End Phase, ie, the turn in which he was destroyed. If you have no Tuners that turn, then you can't activate this effect, and if you pass that turn's End Phase, then you have passed the time to activate it, so it does not matter to Odin if you get a Tuner in your graveyard after that.
Just take a card from your hand and place it in the Graveyard pile. You can only do it when directed to by an effect, or you have more than six cards in hand at the end of your end phase. You can never discard a card for no reason.
graveyard
It will not be destroyed during any End Phase in which it is still face down, but will keep checking every End Phase. If it's ever face up, then it will be destroyed, even if the special summon happened a few turns previously.
Just take a card from your hand and place it in the Graveyard pile. You can only do it when directed to by an effect, or you have more than six cards in hand at the end of your end phase. You can never discard a card for no reason.