> 1. Already being logged in the forum (my own) and
> using the top forum page as start URL.

HTT uses its own browser, it does not share cookies with the browser you used
to sing in with.

> 2. Using the “landing” page, i.e., the ***.com
> page as start URL and giving HTTrack my name and
> password.

View <http://httrack.kauler.com/help/Authentication>
 
Sounds like you might need to use Capture URL on HTT. Another option is to
export your cookies (as a .txt netscape compatible format) for the website
once loged in on your browser over to your project folder. Remember to add
exclude logout rule and possibly make cookie file read only with this method.