I\'m just about to start a new ASP.NET project using MVC3, and since some of the requirements are about facebook integration, I need your advice on the following issues:
I've done something similar recently. Based on my experience:
Yes, you can connect your membership with a Facebook account, however it does not guarantee your user activity will be pushed to Facebook. (users have to log in with Facebook authentication)
Same as above. This blog post does a good job of describing it: http://amirrajan.net/Blog/asp-mvc-and-facebook-single-sign-on
No, facebook connect only takes care of authentication. For more information, check: http://thinkdiff.net/facebook/graph-api-javascript-base-facebook-connect-tutorial/
I have not tried the Facebook SDK you mentioned. However, I believe facebook Graph API already does a good job for you to and will fulfil your requirement