Nope, you got it all wrong

You just need cURL enabled and a firewall or server/computer configuration that lets communicate with facebook.com (for mostly everything) and sourcecoast.com (for configuration only, but not required).
We do almost all of our development from 'localhost' and most of our users seem to use local development first. It makes sense and its safe. Something on your computer though seems to be preventing the basic communication required with the different sites involved.
Since the error your getting is the curl_init is not defined, that means:
* You're using an extremely, extremely old version of PHP. curl_init has been included (by default) in PHP since v4.0.2, which was released in 2001, I believe. This likely is not the case
* The PHP version you have installed was specifically configured *not* to include cURL. Again, it's included by default, so this is something that would have to be excluded intentionally. That seems to be the case. cURL can be excluded during compilation or (I think) through configuration settings which will forcefully disable it.
What are you using for development? Do you have any control over the PHP configuration or how it was installed and configured on your site? If so, you'll need to enable cURL functionality. If not, we'd recommend using something like WAMP (for windows) or something comparable for other OS's.
Hope that helps with some background. Facebook and JFBConnect both can work just about 100% normally on localhost setups. There are some features that won't work on localhost, but those are not the 'basic' features of JFBConnect..
Alex