The favicon mishap can be explained like this:
Look at the link of the icon in your html page source, you will see it uses relative link. Now when you are under site.com/blah/blah2 and you use relative link like that then it can be interpreted that the favicon image is under "blah2" folder.
Since we already set the base href, this should not happen, it's weird that it still happens from time to time on your site, but again this is not a bug. I can assure 100% that this has no effect on what search engine actually crawl. Another way to solve this would be using an absolute link for the favicon (like
http://www.site.com/favicon.ico), dont forget that you need to use https in https pages.
Regarding the rewrite condition on the wiki, it does work as is. You can append the "com" if you want to.
Regarding session, it's just like ssl cert thing I mentioned, www and nonwww are treated differently.