Yes for most of the answers
There is an easy configuration area where you can enable/disable FB Like, Twitter Share, LinkedIn Share, and Google +1 on every article. You can choose to display it above or below the article and also choose whether they should display on that article in a blog view. The same goes for the FB Comments box. So, you should have the flexibility you're looking for there, no problem.
I'm not sure about what you mean by 'working with all types of facebook pages'? The Like button can be used to Like any URL from your website. There is another module, JFBCFan, that lets you show a Like button for your Facebook Fan Page as well as it's stream and user avatars if you want. We don't have any real integration with FB Events right now.
Hope that helps answer your question, but if you have others, just let us know!
Thanks,
Alex