to show the users name, you will need to store it in a session variable. to do this, open the login page, go to the server behaviors panel and double click the Authenticate User server behavior. On the session variable tab, click the plus button and select the User First name and user last name columns.
You can then use the bindings for the first name and last name session variables to show them on your page along with the link tothe profile page
to show or hide areas of the page based on login state, use the security assist show region behavior (Window -> Security Assist - Show Region).
after adding the welcome message and links, select them and add the show region behavior using the "Logged Into <Your User table>" Rule (Where <Your User table> is the name of your user table).
to hide the form, select it, then apply the show region behavior using the "Not Logged into <Your User table>" rule.