Yes... you can Special Summon Exodia the Forbidden One by discarding him and using Monster Reborn, but you will not automatically win the duel. Exodia's effect will only work when it and the other four pieces of Exodia are in your hand.
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A monster's special summon text only applies while it is in your hand. If a monster says it can 'only be' special summoned by a certain method, then assuming you do summon it properly, and it is then destroyed, then you are allowed to use Monster Reborn and do not have to pay any additional costs. If the above monster was simply discarded from hand by something else, then it can not be special summoned by Monster Reborn. If it says 'cannot be special summoned except by..' then it can't be brought back with Monster Reborn even if it was properly special summoned first.
No, Raviel is what is known informally as a 'nomi' monster, meaning there is 'only' one way to summon him, and that's to follow the instructions in his text. This kind of monster can be identified by the text "Cannot be special summoned except by", and these monsters can't be summoned by Monster Reborn, even if you properly summon them, and they are then destroyed.
It's just a regular Lv3 monster, simply place him on the field as a Normal Summon. He is not much use there though as his win condition effect only works when he's in hand.
Only if the card specifically says it can summon a Ritual Monster, like Ritual Foregone. Otherwise, you can't do it, cards like A Hero Emerges, or Monster Gate, cannot special summon a Ritual Monster.Also if you summon the Ritual Monster properly, by Ritual Summon, and it is then sent to the graveyard for whatever reason, then you may bring it back to the field using cards like Monster Reborn. However you cannot simply discard a Ritual Monster from hand and try using Monster Reborn straight away, they are a form of special summon only monster, simply by being Ritual Monsters.
As long as you summoned it with Monster Reborn in main phase 1, then yes, of course. If you summoned it in main phase 2, you cannot attack because you have already passed the battle phase.