1) There is no JDBC support for a remote DB connection on the RIM platform. The general practice is to have some type of web service running on your server which accepts an HTTP request, performs the DB query, and returns the payload as some type of document (XML, JSON, SOAP, whatever). The details are generally dictated by the available server-side infrastructure.
2) You would most lilkely create a Java program which resides on the device. This really depends on the requirements - you might also make a web app.
I suggest that you do some research on the platform and the tools. BlackBerry - BlackBerry Developer Zone