First of all if I would be you then I would make life easy, spawn a zombie prefab using Instantiate instead of making it visible using rendering tag. When you instantiate your character Start method will be called, use this method to follow the player.
Regarding your mesh hierarchy, it depends how you have made your mesh in maya or any other similar software. , it will be visible in same way. If I would be you I would import maya .mb file directly into unity3d like I did in [RabbitBinkies][1].
[1]: https://play.google.com/store/apps/details?id=com.FATechStudio.RabbitBinkies
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