If you toss your starting Animator, Iruki-Waraki will sell you a new one for 10,000 gil.
You must have Automaton Attachments equipped for your Automaton to receive the effects of the attachments when using elemental maneuvers corresponding to the elements of the attachments. However, you still receive slight temporary stat increases for a particular stat of the elemental maneuver if no corresponding attachment is equipped.
Automatons with the Soulsoother Head have the ability to cast beneficial spells on all members of the Puppetmaster's party. (The automaton and master will always have priority over other members.)
In salvage all the Puppets stats are directly tied to the master, ergo having Max HP will limit both Master and Pet, additionally even though the master might have abilities unlocked and a non-mage sub HE WILL REQUIRE magic unlocked in order for his puppet to cast magic with the appropriate frame.