Is the Orb the spellcaster for the copied spell?
Yes.
If I cast a Magic with X in the cost, does the copy have the same value of X too?
Yes. The Orb copies the spell after costs have been paid, so X is a set value.
If I cast a spell with an additional cost (e.g. Craterize), do I need to pay the additional cost again?
No. The Orb copies the spell after costs have been paid.
Can I target the same site twice when casting two copies of Craterize with Orb?
You technically can, but beware! If the first Craterize successfully destroys the targeted site, the second Craterize will no longer have a valid target in the realm and will fail, resulting in no damage from that copy of Craterize.
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