If you have a link to your forum on your website people can click on the link
Your Forum has the title you give to it in your maintenance area for your forum as well.
I am not sure if search engines count forums as websites etc and index them quickly etc if your website is a forum only and not a full out website with links and other stuff besides the forum
Forum website? OK, I guess you mean that you are using or trying to use an embedded forum in your website as you are referring to two different things there.
Bravenet send you the code to embed the forum on the page of your choice. You decide what the web page is called, nobody else.