Hi,
The MySQL support can be considered stable.
It's quite easy to add Activiti to an existing web application. You just have to copy the Activiti Engine JAR and its dependencies. Then you also need to start the Activiti Engine, which is explained in the userguide.
When you need more detailed info you can read my book, Activiti in Action, which explains how to use Activiti in an existing web application.
Best regards,