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No. Copy effects care about the base characteristics of the card. Modifications like that of Figure of Destiny 's abilities or animation effects on noncreature permanents don't apply to the copy. Phantasmal Image will be a 1/1 Kithkin creature no matter what the original Figure of Destiny is at the time.
No, in this case it would become a 1/1 kithkin named Figure of Destiny . It will have all of those abilities though. So if you have the right mana you can eventually make it an 8/8.
Copy effect only ever copy the "base" creature, as Epochalyptik put it. So it won't copy any damage the creature has, any counters, or auras. However if copying a creature that is copying another creature, u will copy the creature that is being copied. Even if the original creature leaves play.