Yes, you can just embed the engine inside your Java application, the installer is a possible architecture with all the tools installed / preconfigured, but you definitely don't need to use it like this. In your case, I assume you would just create a ksession in your Java application code and do invocations directly. The best way to get started is probably to try out some of the Eclipse examples (as they are all just simple Java applications anyway).
1) Yes, we use JPA for configuring persistence, so this typically involves updating the persistence configuration file with updated descriptions on where to find the database, the driver used, etc. You might want to take a look in the quickstarts for some more information:
http://docs.jboss.org/jbpm/v5.4/userguide/ch.installer.html#d0e884
2) You can use a centralized task service, but we also support a local task service now, which is basically a task service running next to the engine and performing all task-related operations. You might want to take a look at for example how the jbpm-test module does this by default:
https://github.com/droolsjbpm/jbpm/blob/5.4.x/jbpm-test/src/main/java/org/jbpm/test/JbpmJUnitTestCase.java#L551
Kris