This familiar is treated as a figure but cannot recover any amount of . It may perform 1 attack action during its activation. Each attack made by this familiar gains:
If the Necromancer is defeated, is his reanimate defeated and removed from the map as well?
No, the reanimate is not defeated when the Necromancer is defeated. Unless specifically noted otherwise, familiars treated as figures are only defeated when they suffer damage equal or greater than their Health.
Can the Necromancer activate his Reanimate familiar at the start of his turn, voluntarily destroy it, spend an action during his turn to create a new Reanimate familiar, and then activate this new Reanimate at the end of his turn?
No, a familiar can only be activated once per round. Even though the Reanimate was removed and placed again, it is still the same familiar.