Hi Michal,
Cool, if you want to create a simple web application that shows the users the different tasks that appears in your processes you can use the jbpm-human-task module that provides an API to get the information about the pending tasks. Using this API you will be interacting with the human task component.
In another place in your application you will need to create a new KnowledgeBase that contains the process definition and a session to execute new instances of that process definition. Because Business Processes that includes human tasks are usually (99.9% of the times) long running processes you will need to share the session between different requests. Here you will have some options, you can have one session per process instance or you can organize multiple process instances in the same session, but it really depends on your processes and your design. For keeping track of which session has each process you will need to write a very thin layer that allows you to interact with the right session and the right process instance.
About integrating the admin console with your struts app, I think that you can, but if you want to modify the admin console you will need to learn GWT. I'm pretty sure that if you know well struts, replicating the code that is inside the admin console should not be difficult, but it is completely up to you.
Cheers