Not true. They are definately discounted when calculating the value of the link but that doesn't affect page rank. The actual value of a link and it's PR value are 2 different things. Not true. See above. True True Not true
Sorry to burst your bubble, but pr means absolutely nothing. It does not determine your traffic to your website. I have lower pr websites making more and bringing more traffic than pr 5 websites.
True. All of your backlinks are quantified by PR so Google can be this single value in the ranking algorithm. And links in content pass more trust and more authority than links in the footer. More information here... http://www.blogstorm.co.uk/google-links-in-content-are-more-valuable/ True. It been well known for over a year know that most directory backlinks are discounted. Absolutely true. Trust and authority are one of the fundamental factors in the pagerank algorithm.
I hate to inform you, but PR is still a major factor in determining the SERP positioning. It's not the only factor, as there are over 200 different factors. But ti's still a major one. One page optimization is always going to be more important than PR. And becuase of on page optimization, a pr0 page can outrank a pr5 page for a specific SERP that the pr0 page is optimized for and the pr5 page isn't.
Ok, I think I know now where your confusion is coming from. In that video Matt Cutts mentions the original page rank and the new algorithm that Google uses today. So here's the revelation: the IE toolbar page rank it's THE ORIGINAL PAGE RANK. Google cannot reveal their new and improved page rank values because they would be revealing their new algorithms.
That's correct. But through various comments form google employees over the last few years, and through extensive testing and reseach, we that work in the SEO industry know many of the new factors that have been introduced into the pagerank algorithm. They haven't used the original algorithm developed by Stanford in probably over 10 years.