Elephant garlic - 3 questions

Got some more elephant garlic bulbs today, 3 questions I have about them.
Some of the blubs have been vut, maybe with a trowel when dug up. Can they be planted or will they rot and are best eaten now?
Some of the bulbs are really quite big, all with roots on. Can I halve them and expect them to grow?
As said, the bulbs are quite big. I guess after a season they will produce a bulb equally big. Is there any benefit in harvesting them after 1 season when all I get is about what I planted. Better to leave them 2 seasons to grow cloves?
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