Bill,
Sorry for the delay. Currently, JFBConnect doesn't offer the features you're looking for, and it's not something we'll likely be adding soon. While it's possible to do, Facebook's terms of service prevent a lot of what you're asking for. Things like 'sweepstakes' and other incentives for users to click the Like or Share button are discouraged (and in many cases straight-out disallowed).
The reasoning is that Facebook wants the sharing features to be 'organic' and not incentivized in any way. They want users to want to share, not be pushed into doing it. It keeps their social graph clean and reinforces the point of sharing so that other users trust it more.
With all that said, we do have 'hooks' on the Like button where you (the administrator) can get an email whenever the Like button is clicked. It'd be easy to change that logic to store the Like in the database, or do something else with it. You'd need a developer to do so, but we could help point you in the right direction for what/where to modify our code.
Hope that helps explain, but if you have any other questions, just let me know.
Thanks,
Alex