The player who creates the Survivor tokens owns them, not Varchild's controller.

Varchild's second ability isn't locked in as Survivor tokens are created. For example, if a player gains control of Varchild, that player's Survivor tokens may attack Varchild's former controller.

Survivor is a creature type. Varchild's second ability affects any creatures your opponents control that happen to be Survivors, not just the Survivor tokens it creates. Similarly, its third ability affects all creatures that happen to be Survivors. A creature that's all creature types is a Survivor.