ASP.NET MVC3 and Facebook integration

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:

1- Is it achievable to connect my Membership users to thier Facebook accounts so whenever a user share/add/comment on an event on my website, I can automatically share these actions using his/her Facebook account?

2- also the ability to create Facebook events when the user create one on my site, and if he/she updates the event information, I may update them on Facebook too.

3- Can this be achieved using Facebook Connect, or this is only to authenticate users using their Facebook accounts?

4- How about using Graph API from my MVC solution, I know that there is a Facebook C# SDK on Codeplex http://facebooksdk.codeplex.com, but will it satisfy my mentioned needs or not.

Thanks in advance.