I don't think it really matters much. I know a lot of high traffic sites that aren't html valid. digitalpoint.com is one of them. .
I think it may, but that's complete speculation... Many larger sites do nothing in the way of SEO at all and rely completely on inbound links, ads, and other means to maintain their internet presence. I have found that looking to the top for a means of deciding what to do SEOwise, is not all that wise. Look for the kings of lesser know products and keywords and do what they do...as they are the ones that are likely doing something right.
to a certain extent yes. But more the fact of valid HTML, rather than 100% WC3 validation. Search engines mark you down if your tags aren't closed properly. So just ensure your basic code is fine. Adding the google webmaster tools' meta info breaks WC3 validation, but I doubt google will mark you down for it So make your main code work fine, but don't try too hard to achieve WC3 greatness.. lol
Well I guess they kind of are, just incase you have left an important tag open such as a H1 tag for example.
Validation will not affect SEO at least in a short term. This was covered by Matt Cutts from Google in one of his videos.. Anyway, its a good practice to have validated codes.