>Is there only a single controller ?

No, there are many controllers. Each is in charge of the object types it is in charge of.

>What happens if [it] goes down?

CRUD of the object types it manages have no effect until the controller returns to service.

>If multiple controllers, how do they coordinate ?

The database is the source of truth. If one controller needs to "coordinate" with another, it will CRUD entries of the object types those other controllers are responsible for. e.g. Deployments beget ReplicaSets beget Pods.