I think you'll be fighting a losing battle if you try to keep from counting your own site as a referrer.  AFAIK, this happens when someone goes directly to your site by typing in the direct url, or when using a shortcut.  If you send out e-mails with links back to your portal it will also count as a referral from your site.  I think it is an interesting number to see because it really measures how well your site is doing on it's own.  It is kind of strange to have it mixed in with the other referring sites though.

By the way, something else that may throw of your stats is if you or someone else links to an image or other resource on your site.  When the other site displays the image it will count as a referral, and as a visit to your site when it may not be anything but someone leeching.

If you still want to get rid of the link back to the home page from your logo then you can do it by removing the logo skin object from your skin and just putting your logo directly in the skin.

Not as far as Google Analytics is concerned.  GA needs the ga.js file to execute in order to record a 'hit' to your site.  Someone linking to an image on your site will only count as a referrer in your actual site logs, not a script-based approach like GA.

But the other part is correct - you will always count your own site as a referrer.  It should be possible in GA to filter this out.  You might also want to use a skin with a hardcoded logo and associated Url, so that you don't have the  /default.aspx Url as a link.  It should either be the site root '/' or the site home page '/home.aspx'.