They have become far less valuable (almost none now) for passing PR, but for internal linking its still a little valuable, especially if there arent very many.  But for the most part footers are no longer valuable - Google cracked down on that a while ago.

Best practice for all three cases is to never use the file extensions.  You should never link to the file extension names, and make sure in your htaccess file that you dont use the file extensions for any reason moving forward.  Why?

1. Lets say you decide to re-do your site and it goes from PHP to another language like ASP or something.  You would have to redirect your entire site with file extensions and would shoot yourself in the foot with SEO, traffic and anything else.  By not using file extensions, you give yourself the flexibility down the road and you can maintain a constant url structure.

2. Indexing may or may not use the file extensions depending on your htaccess/server settings.  You would then essentially be running into duplicate content pages and issues, and thereby negatively affecting your site.  Plus, it will dilute your individual page authority.

As a side note, just be consistent with your internal linking.  Whether you use relative links or not - some discussion can be had around that.  But pick a route and go with it, just as long as you dont use the file extensions

I think you may be getting xml sitemaps confused with sitemap pages.  Your xml sitemap should live at /sitemap.xml as Alan pointed out.   The seomoz and other sites that have a /sitemap page is for different purposes.  Its not your xml file, its a "topical guide" to your website and all the major sections of your site.

Remember that you can also create a xml sitemap index if you need to have different sitemaps (video, news, content) that houses all the different xml sitemaps underneath it.