Rulings

The value of X in Zaxara's last ability is the value of X of the spell you cast.
If the spell you cast has in its mana cost, the token gets only X counters, not twice X.
The Hydra token enters the battlefield as a 0/0 creature. Any abilities that modify or trigger on this event apply. After the token is on the battlefield but before any player can take actions, +1/+1 counters are put onto the token.
If X is 0, the 0/0 Hydra token will die immediately after the ability's done resolving unless something else is raising its toughness.
If an effect, such as that of Parallel Lives, causes Zaxara's ability to create multiple Hydra tokens, they each receive X +1/+1 counters.