OK, I do still have to take issue with the use of Snidget feathers as a core. Causing harm to a Snidget is considered an offence in the Wizarding world on account of how rare they became after being hunted nearly to extinction (think Ivory trade and you're most of the way there) so it's very unlikely that the feathers from one could be used for wand making.

Secondly, as has been pointed out students can't bring snakes with them. The rule is Cat, Owl or Toad.

As for Zac... Are you seriously suggesting he stole someone else's cat?