Dcasmr,
Sorry for the delay, and glad that didn't slow you down from subscribing. I'll answer your questions below, but should you run into any issues, don't hesitate to get in touch!
1) No, we currently don't support pushing content to your Facebook Page. It takes a bit of work, and I wouldn't recommend (even if we did support this) pushing everything back to your FB Page as that could start looking clumsy depending on the amount (and type) of posts you get).
2) I don't believe so. I'm not 100% certain what you mean here, but multiple Like buttons on a page isn't a problem and each can be 'unique'.. and not tied to each other.
3) See #1. Again, we don't do a lot of pushing to Facebook Pages right now, unless you're using the Facebook Page Tab integration where you want to show your site within Facebook itself. We support Page Tab integration very well and have a lot of options for that.
4) There's a ton of ways to configure JFBConnect and integrate Facebook into your site. We'll gladly help if you have any specific questions, but each site is different, and we try to make sure JFBConnect can be easily tailored to any site's needs.
Hope this all helps, and good luck,
Alex