If they duel as it happens in yugioh and exodia gets all five pieces of himself in his hand at once, exodia. But if they were battling, like in pokemon, mewtwo would win for home advantage.
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Just in your hand.
No - as is stated on 'Exodia the Forbidden One' itself, the automatic win is declared when all five parts are in your hand, not on the field.
It really depends upon how much they are trained and which moves they know. Mewtwo is stronger but Mew is more skilled. Presumably, if Mewtwo calmed down a bit and trained more, Mewtwo would have the advantage.
The effect is that you'll win automaticaly if you have all 5 pieces of exodia in your hand.
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.