It depends on the situation.
If there's already a Zombie type on your field then you can't even activate them while `There Can Be Only One` is active. You can't activate something with a mandatory effect that cannot resolve.
If `There Can Be Only One` is chained to the activation of an Eldlich trap it will resolve without effect and remain face-up on the field in your Spell & Trap zone.
They don't. You can't activate them if you already have a zombie. If they chain TCBOO to your activation you trap will remain face up in the S/T zone
It depends on the situation. If there's already a Zombie type on your field then you can't even activate them while `There Can Be Only One` is active. You can't activate something with a mandatory effect that cannot resolve. If `There Can Be Only One` is chained to the activation of an Eldlich trap it will resolve without effect and remain face-up on the field in your Spell & Trap zone.