I start a jbpm instance, load and compile a process, and start a process. In this jbpm instance there is a jbpm-console?
No: jbpm-console uses jbpm runtime, but not the other way around. You can see it this way: jbpm runtime is a bunch of jars you can use in wathever application you want. Jbpm-console is a web application (war) that uses jbpm runtime.
So, for steps 1 and 2, you will need to deploy an instance of jbpm-console instead of create your own web application that uses jbpm-runtime.
Can I attach a jbpm-console to it?
In theory there is a way to do this: both applications (jbpm-console and your own application using the API) must be configured to use the same database and HT server instance. I never tried this before, so I'm not sure if this solution works without any other customization. Maybe someone else that have tried this can help you here.
Best Regards,