Hi Ivan,
I'm fairly new to this stuff myself, but I can help you out with a few definitions. A bean is actually a class itself which must follow a few rules such as it must provide a no-parameter constructor and its properties must have getter and setter methods. So yes, you will be able to use beans in your classes in the same way you would any other class.
An EJB is an Enterprise Java Bean. This is a bean that can be used in a distributed, or enterprise system. There are session EJBs which usually do something and entity EJBs that are used to hold data, and communicate with a database, for example.
J2SE is the standard Java edition which contains all the stuff you would expect for developing a straightforward application. J2EE is the enterprise edition that contains all the support of an enterprise (distributed) system, including EJBs, CORBA and masses more.
I hope this has helped a bit!