Call to action on FB-Fanpage

It's basically a way to create a link directly to your website. JFBConnect isn't involved in how you use that button. Select the call to action and a link on your site to send users to... for example:
* Signup - use a link to your registration page
* Shop Now - use a link to your shopping cart home page, if you use one

I hope that helps explain,
Alex

Yes, but Facebook allows some options, and one of the options is to "use an app".

I'm not exactly sure what that means, but my best guess would be that you can direct a user to your Canvas Application. Most of the time, that's a game that loads within the Facebook Canvas area.. however, it really is just a way to load any page from your website within Facebook, like our Canvas site:
apps.facebook.com/joomla-extensions/
JFBConnect does have some benefits for Canvas sites, like letting you load a special template when in the Canvas view. However, most users would prefer just to send the Facebook guest directly to their site than to a Facebook-surrounded view. That's your choice though.

Can the button be used to anything else then to link something?

That's a new feature of Facebook pages, so I don't know a huge amount about it... as far as I know, it can only link to somewhere else though.

I hope that helps answer your questions,
Alex