>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.

The k/v store offers primitives to make that happen, but for non-critical controllers you don't want to deal with things like that they can go down and will be restarted (locally by kubelet/containerd) or rescheduled. Whatever resource they monitor will just not be touched until they get restarted.