point 6 - Your application runs in a container with, potentially many other app containers on the same Droplet Execution Agent (DEA) - more simply referred to as a VM. If a DEA was to fail in the cloud, then your app containers would be started elsewhere in the cloud (up to the instance count you specify).

Don't get containers confused with VM's Containers are very light-weight and fast to start. VMs are, well, not. :)

As for detection of application down, my experience is like 5 seconds or so. Bluemix may be setting more longer, say 15 seconds at maximum (note: this value is not official). When the application is down, Bluemix core component called Cloud Controller get notified of application down, and it automatically stage new application (and new VM instance(s) based on instance parameters). I recommend to have multiple instances in the production environment so that even if one your application instances is down, the rest will continue to service to your customer (also make the app to recover session)

Takehiko Isn't the health manager responsible for keeping an eye on the applications?

Cloud Controller based on feedback from health manager ensures that the expected number of app instances are running.

To expand on John Pape's comment, the applications run on a warden container (which are light-weight).

The hm9000 doesn't interact or "check" the apps directly. That responsibility is given to the DEA. The DEA is responsible for monitoring the availability of the app containers running on it. This info is passed back to the hm9000 and thus made available for the cloud controller to make decisions on availability.