We do accept Twilight stories, in our Books subdomain, here. I'd also recommend reading the FAQ for Disclaimers, since we do require those, unlike some other fan fiction sites.
If the dark brown at the upper right has your archive pen name showing already, then yes, you are already signed in. You only need to log in if the fields for your email and password are showing, even if your browser has autofilled them. The forum is a separate registration, yes, and you can access that registration at the upper right corner of the forum screen.