As others have said...create a Business Page. You can also join relevant groups from your facebook personal profile.

I do recommend it, as it helps toy to narrow I in on the promotion of your site/business.
Thanks for asking.
Cheers

I have a FB page for my website and I link those 2 together but I always seem to forget about Youtube and I didn't know that was ownned by Google. i really liked your tutorial Hal!

The short answer is YES.

I just blogged the rest here at WA... The Holy Trinity of Internet Marketing

By FB account, do you mean page? If you mean page, I definitely recommend creating a page for your website. If you mean an entirely separate account, then I'd say no. You can manage your facebook page through your personal account.